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Yuzuru Inahama Last modified date:2018.06.13



Graduate School
Undergraduate School


E-Mail
Homepage
http://www2.math.kyushu-u.ac.jp/~inahama/
Academic Degree
Doctor of Science
Field of Specialization
probability theory
Outline Activities
I am studying and teaching mathematics, in particular, probability theory.
Research
Research Interests
  • probability theory
    keyword : rough path theory, Malliavin calculus, stochastic differential equation.
    1995.04~2026.12.
Academic Activities
Papers
1. 稲濱 譲, Malliavin differentiability of solutions of rough differential equations, Journal of Functional Analysis, 267, 1566-1584, 2016.10, In this paper we study rough differential equations
driven by Gaussian rough paths from the viewpoint of Malliavin calculus.
Under mild assumptions on coefficient vector fields and underlying Gaussian processes,
we prove that solutions at a fixed time is smooth in the sense of Malliavin calculus.
Examples of Gaussian processes include fractional Brownian motion with Hurst parameter larger than 1/4..
Presentations
1. 稲濱 譲, Short time full asymptotic expansion of hypoelliptic heat kernel at the cut locus, Cut Locus -- A Bridge Over Differential Geometry Optimal Control and Transport--, 2016.08, We prove a short time asymptotic expansion of a hypoelliptic heat kernel on an Euclidean space and a compact manifold.
We study the "cut locus" case, namely, the case where energy-minimizing paths which join the two points under consideration form not a finite set, but a compact manifold. Under mild assumptions we obtain an asymptotic expansion
of the heat kernel up to any order. Our approach is probabilistic and the heat kernel is regarded as the density of the law of a hypoelliptic diffusion process, which is realized as a unique solution of the corresponding stochastic differential equation. Our main tools are S. Watanabe's distributional Malliavin calculus and T. Lyons' rough path theory.
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Membership in Academic Society
  • Mathematical Society of Japan