| Setsuo Taniguchi | Last modified date：2021.10.08 |
Graduate School
Administration Post
Director of the Admission Center
Vice President
Dean of the Faculty of Arts and Science
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Homepage
https://kyushu-u.pure.elsevier.com/en/persons/setsuo-taniguchi
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http://www.artsci.kyushu-u.ac.jp/~se2otngc/
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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. In particular, I have been making detailed studies on the Grushin operators.
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. In particular, I have been making detailed studies on the Grushin operators.
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
Membership in Academic Society
- 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.
- 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.
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
- the Mathematical Society of Japan
Educational
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