Updated on 2024/03/30

写真a

 
TAGUCHI,Dai
 
Organization
Faculty of Engineering Science Associate Professor
Title
Associate Professor
Homepage
https://sites.google.com/view/daitaguchi/home
External link

Degree

  • 博士 ( 理学 )

Research Areas

  • Natural Science / Applied mathematics and statistics

Professional Memberships

  • 日本数学会

    2013 - Present

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  • 日本金融・証券計量・工学学会

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Papers

  • Semi-implicit Euler–Maruyama scheme for polynomial diffusions on the unit ball Reviewed

    Takuya Nakagawa, Dai Taguchi, Tomooki Yuasa

    Journal of Mathematical Analysis and Applications   519 ( 2 )   126829 - 126829   2023.3

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    Authorship：Lead author   Language：English   Publishing type：Research paper (scientific journal)   Publisher：Elsevier BV  

    DOI： 10.1016/j.jmaa.2022.126829

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  • On the strong convergence rate for the Euler–Maruyama scheme of one-dimensional SDEs with irregular diffusion coefficient and local time Reviewed

    Dai Taguchi

    Journal of Complexity   74   2023.2

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    Authorship：Lead author   Language：English   Publishing type：Research paper (scientific journal)  

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  • Approximations for adapted M-solutions of Type-II backward stochastic Volterra integral equations

    Yushi Hamaguchi, Dai Taguchi

    ESAIM: Probability and Statistics   2022.11

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    Publishing type：Research paper (scientific journal)   Publisher：EDP Sciences  

    In this paper, we study a class of Type-II backward stochastic Volterra integral equations (BSVIEs). For the adapted M-solutions, we obtain two approximation results, namely, a BSDE approximation and a numerical approximation. The BSDE approximation means that the solution of a finite system of backward stochastic differential equations (BSDEs) converges to the adapted M-solution of the original equation. As a consequence of the BSDE approximation, we obtain an estimate for the $L^2$-time regularity of the adapted M-solutions of Type-II BSVIEs. For the numerical approximation, we provide a backward Euler--Maruyama scheme, and show that the scheme converges in the strong $L^2$-sense with the convergence speed of order $1/2$. These results hold true without any differentiability conditions for the coefficients.

    DOI： 10.1051/ps/2022017

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  • $L^{q}$-error estimates for approximation of irregular functionals of random vectors Reviewed

    Dai Taguchi, Akihiro Tanaka, Tomooki Yuasa

    IMA Journal of Numerical Analysis   42 ( 1 )   840 - 873   2022.1

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    Publishing type：Research paper (scientific journal)   Publisher：Oxford University Press (OUP)  

    <title>Abstract</title>
    In Avikainen (2009, On irregular functionals of SDEs and the Euler scheme. Finance Stoch., 13, 381–401) the author showed that, for any $p,q \in [1,\infty )$, and any function $f$ of bounded variation in $\mathbb{R}$, it holds that $ \mathbb{E}[|f(X)-f(\widehat{X})|^{q}] \leq C(p,q) \mathbb{E}[|X-\widehat{X}|^{p}]^{\frac{1}{p+1 } } $, where $X$ is a one-dimensional random variable with a bounded density, and $\widehat{X}$ is an arbitrary random variable. In this article we will provide multi-dimensional versions of this estimate for functions of bounded variation in $\mathbb{R}^{d}$, Orlicz–Sobolev spaces, Sobolev spaces with variable exponents and fractional Sobolev spaces. The main idea of our arguments is to use the Hardy–Littlewood maximal estimates and pointwise characterizations of these function spaces. We apply our main results to analyze the numerical approximation for some irregular functionals of the solution of stochastic differential equations.

    DOI： 10.1093/imanum/draa096

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  • Newton-Kantorovitch method for decoupled forward-backward stochastic differential equations Reviewed

    Dai Taguchi, Takahiro Tsuchiya

    Electronic Journal of Differential Equations   2021 ( 98 )   1 - 16   2021.12

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  • Probability density function of SDEs with unbounded and path-dependent drift coefficient Reviewed

    Dai Taguchi, Akihiro Tanaka

    STOCHASTIC PROCESSES AND THEIR APPLICATIONS   130 ( 9 )   5243 - 5289   2020.9

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：ELSEVIER  

    In this paper, we first prove that the existence of a solution of SDEs under the assumptions that the drift coefficient is of linear growth and path-dependent, and diffusion coefficient is bounded, uniformly elliptic and Holder continuous. We apply Gaussian upper bound for a probability density function of a solution of SDE without drift coefficient and local Novikov condition, in order to use Maruyama-Girsanov transformation. The aim of this paper is to prove the existence with explicit representations (under linear/super-linear growth condition), Gaussian two-sided bound and Holder continuity (under sub-linear growth condition) of a probability density function of a solution of SDEs with path-dependent drift coefficient. As an application of explicit representation, we provide the rate of convergence for an Euler-Maruyama (type) approximation, and an unbiased simulation scheme. (C) 2020 Elsevier B.V. All rights reserved.

    DOI： 10.1016/j.spa.2020.03.006

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  • SEMI-IMPLICIT EULER-MARUYAMA APPROXIMATION FOR NONCOLLIDING PARTICLE SYSTEMS Reviewed

    Hoang-Long Ngo, Dai Taguchi

    ANNALS OF APPLIED PROBABILITY   30 ( 2 )   673 - 705   2020.4

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：INST MATHEMATICAL STATISTICS  

    We introduce a semi-implicit Euler-Maruyama approximation which preserves the noncolliding property for some class of noncolliding particle systems such as Dyson-Brownian motions, Dyson-Ornstein-Uhlenbeck processes and Brownian particle systems with nearest neighbor repulsion, and study its rates of convergence in both L-p-norm and pathwise sense.

    DOI： 10.1214/19-AAP1512

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  • Malliavin calculus for non-colliding particle systems Reviewed

    Nobuaki Naganuma, Dai Taguchi

    STOCHASTIC PROCESSES AND THEIR APPLICATIONS   130 ( 4 )   2384 - 2406   2020.4

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：ELSEVIER  

    In this paper, we use Malliavin calculus to show the existence and continuity of density functions of d-dimensional non-colliding particle systems such as hyperbolic particle systems and Dyson Brownian motion with smooth drift. For this purpose, we apply results proved by Florit and Nualart (1995) and Naganuma (2013) on locally non-degenerate Wiener functionals. (C) 2019 Elsevier B.V. All rights reserved.

    DOI： 10.1016/j.spa.2019.07.005

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  • On a positivity preserving numerical scheme for jump-extended CIR process: the alpha-stable case Reviewed

    Libo Li, Dai Taguchi

    BIT NUMERICAL MATHEMATICS   59 ( 3 )   747 - 774   2019.9

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：SPRINGER  

    We propose a positivity preserving implicit Euler-Maruyama scheme for a jump-extended Cox-Ingersoll-Ross (CIR) process where the jumps are governed by a compensated spectrally positive. Different to the existing positivity preserving numerical schemes for jump-extended CIR or constant elasticity variance process, the model considered here has infinite activity jumps. We calculate, in this specific model, the strong rate of convergence and give some numerical illustrations. Jump extended models of this type were initially studied in the context of branching processes and was recently introduced to the financial mathematics literature to model sovereign interest rates, power and energy markets.

    DOI： 10.1007/s10543-019-00753-8

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  • On the Euler–Maruyama scheme for SDEs with bounded variation and Hölder continuous coefficients" Reviewed

    Hoang-Long Ngo, Dai Taguchi

    Mathematics and Computers in Simulation,   161   102 - 112   2019.7

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    Language：English   Publishing type：Research paper (scientific journal)  

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  • On the Euler-Maruyama scheme for spectrally one-sided Levy driven SDEs with Holder continuous coefficients Reviewed

    Libo Li, Dai Taguchi

    STATISTICS & PROBABILITY LETTERS   146   15 - 26   2019.3

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：ELSEVIER SCIENCE BV  

    We study in this article the strong rate of convergence of the Euler-Maruyama scheme and associated with the jump-type equation introduced in Li and Mytnik (2011). We obtain the strong rate of convergence under similar assumptions for strong existence and pathwise uniqueness. Models of this type can be considered as a generalization of the CIR (Cox-Ingersoll-Ross) process with jumps. (C) 2018 Elsevier B.V. All rights reserved.

    DOI： 10.1016/j.spl.2018.10.017

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  • On the Euler-Maruyama Scheme for Degenerate Stochastic Differential Equations with Non-sticky Condition Reviewed

    Dai Taguchi, Akihiro Tanaka

    SEMINAIRE DE PROBABILITES L   2252   165 - 185   2019

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：SPRINGER INTERNATIONAL PUBLISHING AG  

    The aim of this paper is to study weak and strong convergence of the Euler-Maruyama scheme for a solution of one-dimensional degenerate stochastic differential equation dX(t) = sigma(X-t)dW(t) with non-sticky condition. For proving this, we first prove that the Euler-Maruyama scheme also satisfies non-sticky condition. As an example, we consider stochastic differential equation dX(t) = vertical bar X-t vertical bar(alpha)dW(t), alpha is an element of (0, 1/2) with non-sticky boundary condition and we give some remarks on CEV models in mathematical finance.

    DOI： 10.1007/978-3-030-28535-7_9

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  • Convergence Implications via Dual Flow Method Reviewed

    Takafumi Amaba, Dai Taguchi, Go Yuki

    MARKOV PROCESSES AND RELATED FIELDS   25 ( 3 )   533 - 568   2019

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：POLYMAT  

    Given a one-dimensional stochastic differential equation, one can associate to this equation a stochastic flow on [0, +infinity), which has an absorbing barrier at zero. Then one can define its dual stochastic flow. In [2], Akahori and Watanabe showed that its one-point motion solves a corresponding stochastic differential equation of Skorokhod-type. In this paper, we consider a discretetime stochastic-flow which approximates the original stochastic flow. We show that under some assumptions, one-point motions of its dual flow also approximates the corresponding reflecting diffusion. We prove and use relations between a stochastic flow and its dual in order to obtain weak and strong approximation results related to stochastic differential equations of Skorokhod-type.

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  • Approximation for non-smooth functionals of stochastic differential equations with irregular drift Reviewed

    Hoang-Long Ngo, Dai Taguchi

    JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS   457 ( 1 )   361 - 388   2018.1

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：ACADEMIC PRESS INC ELSEVIER SCIENCE  

    This paper aims at developing a systematic study for the weak rate of convergence of the Euler-Maruyama scheme for stochastic differential equations with very irregular drift and constant diffusion coefficients. We apply our method to obtain the rates of approximation for the expectation of various non-smooth functionals of both stochastic differential equations and killed diffusion. We also apply our method to the study of the weak approximation of reflected stochastic differential equations whose drift is Holder continuous. (c) 2017 Elsevier Inc. All rights reserved.

    DOI： 10.1016/j.jmaa.2017.08.006

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  • On the Euler-Maruyama approximation for one-dimensional stochastic differential equations with irregular coefficients Reviewed

    Hoang-Long Ngo, Dai Taguchi

    IMA JOURNAL OF NUMERICAL ANALYSIS   37 ( 4 )   1864 - 1883   2017.10

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：OXFORD UNIV PRESS  

    We study the strong rates of the Euler-Maruyama approximation for one-dimensional stochastic differential equations whose drift coefficient may be neither continuous nor one-sided Lipschitz and whose diffusion coefficient is Holder continuous. In particular, we show that the strong rate of the Euler-Maruyama approximation is 1/2 for a large class of equations whose drift is not continuous. We also provide the strong rate for equations whose drift is Holder continuous and diffusion is nonconstant.

    DOI： 10.1093/imanum/drw058

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  • Strong rate of convergence for the Euler-Maruyama approximation of SDEs with Holder continuous drift coefficient Reviewed

    Olivier Menoukeu Pamen, Dai Taguchi

    STOCHASTIC PROCESSES AND THEIR APPLICATIONS   127 ( 8 )   2542 - 2559   2017.8

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：ELSEVIER SCIENCE BV  

    In this paper, we consider a numerical approximation of the stochastic differential equation (SDE)
    X-t = x(0) +integral(t)(0) b(s, X-s)ds + L-t, x(0) is an element of R-d., t is an element of [0, T],
    where the drift coefficient b : [0, T] x R-d -&gt; R-d is Holder continuous in both time and space variables and the noise L =(L-t)(0 &lt;= t &lt;= T) is a d-dimensional Levy process. We provide the rate of convergence for the Euler-Maruyama approximation when L is a Wiener process or a truncated symmetric a -stable process with alpha is an element of (1, 2). Our technique is based on the regularity of the solution to the associated Kolmogorov equation. Crown Copyright (C) 2016 Published by Elsevier B.V. All rights reserved.

    DOI： 10.1016/j.spa.2016.11.008

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  • Strong convergence for the Euler-Maruyama approximation of stochastic differential equations with discontinuous coefficients Reviewed

    Hoang-Long Ngo, Dai Taguchi

    STATISTICS & PROBABILITY LETTERS   125   55 - 63   2017.6

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：ELSEVIER SCIENCE BV  

    In this paper we study the strong convergence for the Euler-Maruyama approximation of a class of stochastic differential equations whose both drift and diffusion coefficients are possibly discontinuous. (C) 2017 Elsevier B.V. All rights reserved.

    DOI： 10.1016/j.spl.2017.01.027

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  • The Parametrix Method for Skew Diffusions Reviewed

    Arturo Kohatsu-Higa, Dai Taguchi, Jie Zhong

    POTENTIAL ANALYSIS   45 ( 2 )   299 - 329   2016.8

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：SPRINGER  

    In this article, we apply the parametrix method in order to obtain the existence and the regularity properties of the density of a skew diffusion and provide a Gaussian upper bound. This expansion leads to a probabilistic representation.

    DOI： 10.1007/s11118-016-9547-0

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  • STRONG RATE OF CONVERGENCE FOR THE EULER-MARUYAMA APPROXIMATION OF STOCHASTIC DIFFERENTIAL EQUATIONS WITH IRREGULAR COEFFICIENTS Reviewed

    Hoang-Long Ngo, Dai Taguchi

    MATHEMATICS OF COMPUTATION   85 ( 300 )   1793 - 1819   2016.7

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：AMER MATHEMATICAL SOC  

    We consider the Euler-Maruyama approximation for multi-dimensional stochastic differential equations with irregular coefficients. We provide the rate of strong convergence where the possibly discontinuous drift coefficient satisfies a one-sided Lipschitz condition and the diffusion coefficient is Holder continuous and uniformly elliptic.

    DOI： 10.1090/mcom3042

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  • Stability Problem for One-Dimensional Stochastic Differential Equations with Discontinuous Drift Reviewed

    Dai Taguchi

    SEMINAIRE DE PROBABILITES XLVIII   2168   97 - 121   2016

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：SPRINGER INT PUBLISHING AG  

    We consider one-dimensional stochastic differential equations (SDEs) with irregular coefficients. The goal of this paper is to estimate the L-p(Omega)-difference between two SDEs using a norm associated to the difference of coefficients. In our setting, the (possibly) discontinuous drift coefficient satisfies a one-sided Lipschitz condition and the diffusion coefficient is bounded, uniformly elliptic and Holder continuous. As an application of this result, we consider the stability problem for this class of SDEs.

    DOI： 10.1007/978-3-319-44465-9_4

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Presentations

  • CIR過程の数値解析について Invited

    Dai Taguchi

    2022年度中之島ワークショップ 金融工学・数理計量ファイナンスの諸問題 2022  2022.12 

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    Language：Japanese   Presentation type：Oral presentation (general)  

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  • Avikainen の不等式と確率数値解析 Invited

    Dai Taguchi

    関西大学 確率論研究会 2022  2022.11 

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    Language：Japanese   Presentation type：Oral presentation (general)  

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  • Approximation for Lévy driven SDEs with irregular coefficient Invited

    Dai Taguchi

    MATRIX conference  2022.11 

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    Language：English   Presentation type：Oral presentation (general)  

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  • Avikainen’s estimate and its application to numerical analysis for SDEs Invited

    Dai Taguchi

    Seminar on Probability and Mathematical Statistics at Vietnam Academy of Science and Technology Institute of Mathematics  2022.5 

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    Language：English   Presentation type：Oral presentation (general)  

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  • Numerical schemes for Dyson’s Brownian motions and radial Dunkl processes Invited

    Dai Taguchi

    Theory of Markov Semigroups and Schrödinger Operators seminar  2022.4 

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    Language：English   Presentation type：Oral presentation (general)  

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  • Numerical schemes for radial Dunkl processes Invited

    Dai Taguchi

    MFO-RIMS Tandem Workshop  2022.3 

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    Language：English   Presentation type：Oral presentation (general)  

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  • Numerical schemes for radial Dunkl processes

    田口大

    確率解析とその周辺  2021.11 

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    Presentation type：Oral presentation (general)  

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  • Numerical schemes for radial Dunkl processes Invited

    Dai Taguchi

    AIMS Ghana's Online Research Seminar Series  2021.10 

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    Presentation type：Oral presentation (invited, special)  

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  • Backward and truncated Euler--Maruyama schemes for radial Dunkl processes Invited

    Dai Taguchi

    International Conference on Monte Carlo Methods and Applications  2021.8 

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    Presentation type：Oral presentation (general)  

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  • 確率微分方程式の数値解析, Euler–Maruyama 近似の近年の話題 Invited

    田口大

    日本数学会2021年度年会  2021.3 

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    Presentation type：Oral presentation (invited, special)  

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  • Multi-dimensional Avikainen's estimates

    田口大

    確率解析とその周辺  2020.11 

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    Presentation type：Oral presentation (general)  

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  • Multi-dimensional Avikainen's estimates Invited

    Dai Taguchi

    14th International Conference on Monte Carlo and Quasi-Monte Carlo  2020.8 

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    Presentation type：Oral presentation (general)  

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  • Multi-dimensional Avikainen's estimates

    田口大

    大阪大学確率論セミナー  2020.7 

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    Presentation type：Oral presentation (general)  

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  • Multi-dimensional Avikainen's estimates Invited

    Dai Taguchi

    Monash Probability and Statistics Seminar  2020.7 

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    Presentation type：Oral presentation (invited, special)  

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  • Multi-dimensional Avikainen's estimates Invited

    Dai Taguchi

    Probability Seminar of Toulouse  2020.5 

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    Presentation type：Oral presentation (invited, special)  

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  • Multi-dimensional Avikainen's estimates Invited

    田口大

    立命館大学ファイナンスセミナー  2020.4 

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  • A generalized Avikainen’s estimate and its applications

    田口大

    確率論シンポジウム  2019.12 

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  • A generalized Avikainen’s estimate and its applications Invited

    田口大

    第七回数理ファイナンス合宿型セミナー  2019.11 

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    Presentation type：Oral presentation (invited, special)  

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  • Implicit Euler-Maruyama scheme for radial Dunkl processes

    田口大

    確率解析とその周辺  2019.11 

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  • Implicit Euler--Maruyama scheme for radial Dunkl processes

    田口大

    確率論ヤングサマーセミナー 2019  2019.8 

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  • Implicit Euler--Maruyama scheme for radial Dunkl processes

    田口大

    九州確率論セミナー  2019.7 

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    Presentation type：Oral presentation (general)  

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  • Probability density function of SDEs with unbounded and path--dependent drift coefficient Invited

    Dai Taguchi

    ICIAM Congress (the international Congress of Industrial and Applied Mathematics  2019.7 

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    Presentation type：Oral presentation (general)  

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  • On the Euler-Maruyama scheme for degenerate SDEs with non-sticky boundary condition Invited

    Dai Taguchi

    Stochastic processes and related topics  2019.7 

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    Presentation type：Oral presentation (invited, special)  

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  • Probability density function of SDEs with unbounded and path--dependent drift coefficient Invited

    田口大

    関西大学 確率論セミナー,  2019.5 

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  • Jump型CIR過程の離散近似について Invited

    田口大

    金融工学・数理計量ファイナンスの諸問題 2018  2018.11 

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    Presentation type：Oral presentation (invited, special)  

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  • Probability density function of SDEs with unbounded and path--dependent drift coefficient

    田口大

    確率解析とその周辺  2018.11 

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  • On a positivity preserving scheme for the alpha-CIR process" Invited

    Dai Taguchi

    Ritsumeikan Workshop on Probability Theory and its Applications to Insurance and Finance,  2018.10 

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    Presentation type：Oral presentation (invited, special)  

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  • Semi-implicit Euler-Maruyama scheme for non-colliding particle systems Invited

    Dai Taguchi

    The 12th AIMS Conference on Dynamical Systems, Differential Equations and Applications  2018.7 

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    Presentation type：Oral presentation (general)  

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  • Semi-implicit Euler-Maruyama scheme for non-colliding particle systems Invited

    Dai Taguchi

    13th International Conference in Monte Carlo & Quasi-Monte Carlo Methods in Scientific Computing,  2018.7 

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    Presentation type：Oral presentation (invited, special)  

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  • Gaussian bound for the density of SDEs with unbounded and path-dependent drift Invited

    田口大

    福岡大学確率論セミナー  2018.6 

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  • Newton's method for BSDEs

    田口大

    大阪大学確率論セミナー  2018.5 

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  • Implicit Euler-Maruyama scheme for non-colliding particle systems Invited

    Dai Taguchi

    Workshop on "Mathematical finance and related issues", Osaka University Nakanoshima Center  2018.3 

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  • Discrete approximations for non-colliding SDEs",

    田口大

    確率解析シンポジウム  2017.10 

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  • 確率微分方程式の解の一意性について Invited

    田口大

    確率論ヤングサマーセミナー  2017.8 

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    Presentation type：Oral presentation (invited, special)  

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  • On the Euler-Maruyama scheme for SDEs with discontinuous diffusion coefficient" Invited

    Dai Taguchi

    International Conference on Monte Carlo Methods and Applications  2017.7 

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  • Semi-implicit Euler-Maruyama scheme for non-colliding particle systems

    田口大

    九州確率論セミナー  2017.6 

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  • Semi-implicit Euler-Maruyama scheme for non-colliding particle systems Invited

    Dai Taguchi

    Osaka-UCL Workshop on Stochastics, Numerics and Risk  2017.3 

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  • On the Euler-Maruyama scheme for SDEs with irregular coefficients

    田口大

    確率論早春セミナー  2017.3 

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  • On the Euler-Poisson scheme for SDEs with positive jumps and Holder continuous coecient

    田口大

    日本数学会  2017.3 

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  • On the Euler-Maruyama scheme for SDEs with discontinuous diffusion coefficient

    田口大

    岡山確率論セミナー  2017.1 

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  • On the Euler-Maruyama scheme for SDEs with discontinuous diffusion coefficien

    田口大

    確率解析とその周辺  2016.11 

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  • Euler Maruyama scheme for SDEs with discontinuous diffusion coefficient

    田口大

    日本数学会  2016.9 

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  • Euler-Maruyama scheme for SDEs with fractional differential drift

    Dai Taguchi

    Workshop: Stochastic processes - numerical methods and related topics, Hanoi  2016.8 

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  • Euler-Maruyama scheme for SDEs with dis-continuous diffusion coefficient

    田口大

    確率論ヤングサマーセミナー  2016.8 

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  • Euler-Maruyama approximation for SDEs with irregular coefficients

    Dai Taguchi

    Statistics Seminar, UNSW  2016.8 

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  • On the Euler-Maruyama scheme for SDEs with irregular coefficients

    Dai Taguchi

    The Fourth Asian Quantitative Finance Conference  2016.2 

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  • Euler-Maruyama approximation for SDEs with bounded p-variation drift

    田口

    大阪大学確率論セミナー  2016.2 

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  • On the Euler-Maruyama approximation for one-dimensional SDEs with irregular coefficients

    田口大

    確率論シンポジウム  2015.12 

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  • Weak and Strong rate for the Euler-Maruyama scheme for SDEs with irregular coefficients

    田口大

    数理ファイナンス合宿型セミナー  2015.11 

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  • Parametrix method for skew diffusions

    田口大

    確率解析とその周辺  2015.10 

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  • Parametrix method for skew diffusions

    Dai Taguchi

    Probability and Applied Mathematics Seminar, Hanoi  2015.9 

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  • Approximation for non-smooth functionals of SDEs with irregular drift

    田口大

    日本数学会  2015.9 

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  • The rate of convergence for the Euler scheme for stochastic differential equation with irregular drift"

    Dai Taguchi

    Workshop on Quantum Information Theory and related Topics, Hanoi  2015.9 

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  • Numerical Results for Stochastic Differential Equations via Parametrix Method

    田口大

    The Japanese Association of Financial Econometrics and Engineering  2015.8 

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  • Weak approximation for non-smooth functionals of SDEs with irregular drift

    Dai Taguchi

    5th-Ritsumeikan-Monash Symposium on Probability and Related Fields  2015.3 

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  • Weak approximation for non-smooth functionals of SDEs with irregular drift

    田口大

    確率論早春セミナー  2015.3 

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  • Parametrix method for skew diffusions

    田口大

    日本数学会  2015.3 

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  • Strong Rate of Convergence for the Euler-Maruyama Approximation of Stochastic Differential Equations with Irregular Coefficients

    Dai Taguchi

    The Quantitative Methods in Finance 2014 Conference  2014.12 

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  • Stability problem for SDEs with discontinuous drift

    田口大

    確率論ヤングサマーセミナー  2014.8 

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  • Strong Rate of Euler-Maruyama Approximation for Stochastic Differential Equations with Irregular Coefficients

    田口大

    日本数学会  2014.3 

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  • Strong Rate of Euler-Maruyama Approximation for Stochastic Differential Equations with Irregular Coefficients"

    田口大

    数理ファイナンス合宿型セミナー  2014.1 

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  • Strong Rate of Euler-Maruyama Approximation for Stochastic Differential Equations with Irregular Drift

    Dai Taguchi

    The 45th ISCIE International Symposium on Stochastic Systems Theory and Its Applications  2013.11 

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  • Strong Rate of Euler-Maruyama Approximation for Stochastic Differential Equations with Irregular Drift

    田口大

    日本応用数理学会  2013.9 

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  • Strong Rate of Euler-Maruyama Approximation for Stochastic Differential Equations with Irregular Drift

    田口大

    確率論ヤングサマーセミナー  2013.8 

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  • Euler-Maruyama Approximation for Stochastic Differential Equations with discontinuous drift

    田口大

    確率論早春セミナー,  2013.3 

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Research Projects

  • Equations with renormalization and stochastic analysis

    Grant number：21H00988  2021.4 - 2026.3

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research  Grant-in-Aid for Scientific Research (B)

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    Grant amount：\16900000 （ Direct Cost: \13000000 、 Indirect Cost：\3900000 ）

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  • 非有界係数を持つ経路依存型・非衝突型の確率微分方程式の数値解析と密度関数の研究

    Grant number：19K14552  2019.4 - 2023.3

    日本学術振興会  科学研究費助成事業  若手研究

    田口 大

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    Grant amount：\4030000 （ Direct Cost: \3100000 、 Indirect Cost：\930000 ）

    本研究の目的は、非有界な係数を持つ確率微分方程式と非衝突確率過程の「数値計算手法の構成と誤差評価」を研究することである。2021年度は以下の2点について研究成果を得ている。①Polynomial diffusionsと呼ばれる拡散係数が1/2-ヘルダー連続な場合の多次元確率微分方程式の離散近似手法。②拡散係数が不連続関数である場合の1次元確率微分方程式に対するEuler--Maruyama近似の誤差評価。
    ①について。中川卓也氏（立命館大学）、湯浅智意氏（東京都立大学）との共同研究である。拡散係数が1/2-ヘルダー連続である場合の確率微分方程式の解の存在と一意性は、高次元の場合は特別な場合しか知られていない。その方程式の一つとしてPolynomial diffusionsがあり、その離散近似を導入し誤差評価に関する結果を得た。1次元の場合であればLamperti変換を用いて拡散係数のヘルダー連続性をドリフト係数の問題に置き換えることがでる。一方で多次元の場合には同様の変換を用いることができたいため解の一意性を証明する際に用いられている別の変換手法を適用することで拡散係数のヘルダー連続性をドリフト係数の問題に置き換えることができる。本研究ではこの変換を元に数値解析手法を導入した。
    ②について。1次元確率微分方程式は拡散係数が不連続な関数であっても道ごとの一意性が成立することが証明されている。しかし、これまでの研究では不連続性の問題点から、その数値解析手法であるEuler--Maruyama近似は特別な場合でのみ誤差評価が与えられていた。
    本研究ではAvikainenによって証明された不等式を適用することによって局所時間に関する議論と組み合わせることで道ごとの一意性が成立する条件の元でEuler--Maruyama近似の誤差評価に関する結果を得た。
    ①②共に学術雑誌に投稿済みである。

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  • Numerical analysis for SDE and non-colliding stochastic processes

    Grant number：17H06833  2017.8 - 2019.3

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research  Grant-in-Aid for Research Activity Start-up

    Taguchi Dai, Li Libo, Ngo Hoang-Long, Naganuma Nobuaki, Tanaka Akihiro

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    Grant amount：\2730000 （ Direct Cost: \2100000 、 Indirect Cost：\630000 ）

    Recently, CIR processes (Cox-Ingersoll-Ross processes) and CEV processes (constant elasticity of variance processes) are widely used in mathematical finance, and are extended in various directions, such as extending to the Jump type by using the Levy processes. These stochastic processes have some boundary conditions, such as not taking negative values or not staying at the boundary. The research achievements of this study are to introduce a discrete approximation scheme with the same boundary conditions as these stochastic processes, and provide their rate of convergence.

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