Setsuo Taniguchi | Last modified date：2020.05.11 |

Graduate School

Administration Post

Dean of the Faculty of Arts and Science

Vice President

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Academic Degree

Doctor of Science

Country of degree conferring institution (Overseas)

No

Field of Specialization

Stochastic Analysis and its application

Total Priod of education and research career in the foreign country

02years06months

Outline Activities

I have been studying and teaching Stochastic Analysis, especially Stochastic Complex Analysis. Just after Feynman

developed his famous path integral, M. Kac pointed out that the Wiener integral is the counter part to it. In particular, a stochastic oscillatory integral is the one to Feynman path integral representation of propergator. The asymptotic behavior of stochastic oscillatory integral relates to the semi-classical limits. I introduced a new complixification of the path space and established complex change of variables formulae. With these, I am studying the principle of tationary phase on the path space. I am also invetigating the KdV equations via stochatic oscillatory integrals. Moreover, I recently obtained a diffusion process on a sub-Riemannian manifold by rolling the manifold, and have been investigating the properties of the process and its applications to sub-laplacian analysis.

I have been teaching to graduate students about stochastic models appearing in Mathematical Finance. Moreover, in the joint work with the Nisshin Fire & Marine Insurance Co., I investigated stochastic models in the non-life insurance during AY2008-2012.

developed his famous path integral, M. Kac pointed out that the Wiener integral is the counter part to it. In particular, a stochastic oscillatory integral is the one to Feynman path integral representation of propergator. The asymptotic behavior of stochastic oscillatory integral relates to the semi-classical limits. I introduced a new complixification of the path space and established complex change of variables formulae. With these, I am studying the principle of tationary phase on the path space. I am also invetigating the KdV equations via stochatic oscillatory integrals. Moreover, I recently obtained a diffusion process on a sub-Riemannian manifold by rolling the manifold, and have been investigating the properties of the process and its applications to sub-laplacian analysis.

I have been teaching to graduate students about stochastic models appearing in Mathematical Finance. Moreover, in the joint work with the Nisshin Fire & Marine Insurance Co., I investigated stochastic models in the non-life insurance during AY2008-2012.

Research

**Research Interests**

- Stochastic analysis on sub-Riemannian manifolds

keyword : Sub-Riemannian manifold, stochastic analysis

2017.01. - Stochastic analysis on CR-manifolds

keyword : Stochatic differential equation, CR-manifold, Stochastic differential geometry

2011.10. - Applications of Stochastic Analysis to the KdV equation

keyword : Stochastic analysis, KdV equation, Cameron-Martin transformation

2001.09Expressing the soliton solutions of the KdV equation in terms of the Wiener integral Find the relationship between the tau functions and the Wiener integral Extending to another nonlinear PDE. - Study on asymptotic behaviors of stochastic oscillatory integrals

keyword : stochastic oscillatory integral, statinary phase method, quadratic Wiener functional

1995.07A complexification of the Wiener space and analysis of analytic functions on it, Establishing an explicit expression for quadratic phase functions Showing the localization for quadratic phase functions Establishing the stationary phase method on the Wiener space Appling to the semi-classical limits.

**Current and Past Project**

- Revisiting and developing the nature of mathematics that it is a common langage for sicence, the project contributes all scientific activites. Moreover, it will discover new mathematical viewpoints and/or theories and help the development of mathematical science.

**Academic Activities**

**Books**

1. | Hiroyuki Matumoto, Setsuo Taniguchi, Stochastic Analysis -- Itô and Malliavin Calculus in Tandem, Cambridge Univ. Press, https://doi.org/10.1017/9781316492888, 2017.01, [URL], Thanks to the driving forces of the Itô calculus and the Malliavin calculus, stochastic analysis has expanded into numerous fields including partial differential equations, physics, and mathematical finance. This book is a compact, graduate-level text that develops the two calculi in tandem, laying out a balanced toolbox for researchers and students in mathematics and mathematical finance. The book explores foundations and applications of the two calculi, including stochastic integrals and differential equations, and the distribution theory on Wiener space developed by the Japanese school of probability. Uniquely, the book then delves into the possibilities that arise by using the two flavors of calculus together. Taking a distinctive, path-space-oriented approach, this book crystallizes modern day stochastic analysis into a single volume.. |

**Papers**

**Membership in Academic Society**

- the Mathematical Society of Japan

Educational

**Educational Activities**

I taught Kikan Kyoiku Seminar and Kadai-Kyogaku for freshmen, and am teaching statistics for a undergraduate course students.

For Graduate School of Mathematics, I mainly teaching Stochastic

Analysis. I have taught Stochastic Differential Equations,

Introduction to Probability Theory, and Applied Mathematics III.

To the undergraduate Mathematics students, I have taught

Sugaku Gairon II, Sugaku B2, Sugaku C2, Sugaku Tokuron 10.

To the undergaduate Engineering students, I taught Applied

Probability. To the graduate Engineering students, I taught

Applied Mathematics C. My graduate students are studying

Stochstic Analysis and stochastic differential equations

with applications to mathematical finance.

For Graduate School of Mathematics, I mainly teaching Stochastic

Analysis. I have taught Stochastic Differential Equations,

Introduction to Probability Theory, and Applied Mathematics III.

To the undergraduate Mathematics students, I have taught

Sugaku Gairon II, Sugaku B2, Sugaku C2, Sugaku Tokuron 10.

To the undergaduate Engineering students, I taught Applied

Probability. To the graduate Engineering students, I taught

Applied Mathematics C. My graduate students are studying

Stochstic Analysis and stochastic differential equations

with applications to mathematical finance.

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