Kyushu University Academic Staff Educational and Research Activities Database
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Setsuo Taniguchi Last modified date:2019.05.10



Graduate School
Administration Post
Vice President
Dean of the Faculty of Arts and Science


E-Mail
Homepage
http://www.artsci.kyushu-u.ac.jp/~se2otngc/
List of publications, Preprints, Lecture Notes and more are available .
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.
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
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., 10.1006/jfan.1996.2989, 143, 2, 470-528, 143-2, 470-528, 1997.01.
4. Shigeo Kusuoka and Setsuo Taniguchi, Pseudoconvex domains in almost complex abstract Wiener spaces, J. Funct. Anal., 10.1006/jfan.1993.1123, 117, 1, 62-117, 117-1, 62-117, 1993.01.
5. Setsuo Taniguchi, Explosion problem for holomorphic diffusion processes and its applications, Osaka J. Math., 26, 4, 931-951, 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, 10.1007/BF00532483, 65, 2, 269-290, 65-2, 269-290, 1983.01.
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.