| Setsuo Taniguchi | Last modified date：2013.4.24 |
Graduate School
Undergraduate School
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Academic Degree
Doctor of Science
Field of Specialization
Stochastic Analysis and its application
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 CR-manifold by rolling the manifold, and have been investigating the properties of the process.
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 am investigating stochastic models in the non-life insurance.
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 CR-manifold by rolling the manifold, and have been investigating the properties of the process.
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 am investigating stochastic models in the non-life insurance.
Research
Research Interests
Membership in Academic Society
- 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
2001.09. - Study on asymptotic behaviors of stochastic oscillatory integrals
keyword : stochastic oscillatory integral, statinary phase method, quadratic Wiener functional
1995.07.
- 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.
Papers
| 1. | Setsuo Taniguchi,On the Jacobi field approach to stochastic oscillatory integrals with quadratic phase function,Kyushu Jour. Mathematics,61-1, 191-208,2007.03. |
| 2. | Setsuo Taniguchi,Brownian sheet and reflectionless potentials,Stoch. Pro. Appl,116-2, 293-309,2006.01. |
| 3. | Paul Malliavin and Setsuo Taniguchi,Analytic functions, Cauchy formula, and stationary phase on a real abstract Wiener space,J. Funct. Anal.,Vol.143,No.2,143-2, 470-528,1997.01. |
| 4. | Shigeo Kusuoka and Setsuo Taniguchi,Pseudoconvex domains in almost complex abstract Wiener spaces,J. Funct. Anal.,Vol.117,No.1,117-1, 62-117,1993.01. |
| 5. | Setsuo Taniguchi,Explosion problem for holomorphic diffusion processes and its applications,Osaka J. Math.,Vol.26,No.4,26-4, 931-951,1989.01. |
| 6. | Setsuo Taniguchi,Malliavin's stochastic calculus of variations for manifold-valued Wiener functionals and its applications,Z. Wahrsch. Verw. Gebiete,Vol.65,No.2,65-2, 269-290,1983.01. |
- the Mathematical Society of Japan
Educational
Educational Activities
I am teaching mathematics 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.
The fact that no permission it reprints contents of this data base is prohibitted.