Hiroshi KAWABI
.
.
Position:
Associate Professor
Affiliation:
Department of Mathematics,
Faculty of Science,
Okayama University, JAPAN
email:
myfamilyname AT math.okayamau.ac.jp
Degree: Ph.D. in Mathematical Sciences,
The University of Tokyo (March, 2004)
Thesis:
Topics on analysis for certain infinite dimensional diffusion processes
(Research Advisers: Shigeo KUSUOKA (Univ. Tokyo) and
Shigeki AIDA
(Tohoku Univ.))
Erdös number: 4
P. Erdös

P. Diaconis

D.W. Stroock

S. Aida

H. Kawabi
Research Interests

Stochastic analysis
for infinite dimensional diffusion processes

Stochastic partial differential equations

Malliavin calculus and its application for mathematical sciences
 Rough path analysis and its applications to stochastic analysis

Calculus of variations and nonlinear partial differential equations
Profile
Education
 1988/4  1991/3,
KeioShiki High School.
 1991/4  1995/3,
Faculty of Economics,
Keio University.
Bachelor of Economics, March 1995.
 1995/4 1997/3,
Department of Mathematics,
Graduate School of Science and Technology,
Keio University.
Master of Science, March 1997.
 1997/4  1999/3,
Division of Mathematics,
Graduate School of Information Sciences,
Tohoku University.
Master of Information Sciences, March 1999.
 1999/4  2004/3,
Graduate School of Mathematical Sciences,
The University of Tokyo.
Ph.D. in Mathematical Sciences, March 2004.
Research and Professional Experience
 2007/4
Associate Professor, Department of Mathematics, Faculty of Science,
Okayama University
Research Papers

Short
time asymptotics of a certain infinite dimensional diffusion process
,
(with
Shigeki AIDA),
Stochastic Analysis and Related Topics VII: Proceeding of 7th Silvri Workshop
(L. Decreusefond, B. Oksendal and A. S. Ustunel eds.),
Progress in Probability, volume 48,
Birkhauser (2001), pp. 77124.

Functional
inequalities and an application for parabolic stochastic
partial differential equations containing
rotation,
Bulletin des Sciences Mathematiques, volume 128 (2004), no. 8,
pp. 687725.

The
parabolic Harnack inequalities for the time dependent
GinzburgLandau type SPDE and
its application
,
Potential Analysis
, volume 22 (2005), no. 1, pp. 6184.

On
a
construction of weak solutions to nonstationary Stokes type
equations by minimizing variational
functionals and their regularity,
Commentationes Mathematicae Universitatis Carolinae,
volume 46 (2005) no. 1, pp. 161178.

A
simple proof of the logSobolev inequality on the path space
with Gibbs measures,
Infinite Dimensional Analysis, Quantum Probability and
Related Topics
(IDAQP) , volume 9 (2006), no. 2, pp. 321329.

Large
deviations for heat kernel measures on loop spaces
via rough paths
,
(with
Yuzuru INAHAMA),
Journal of the London Mathematical Society (2),
volume 73 (2006), no. 3, pp. 797816.

Essential
selfadjointness
of Dirichlet operators on a path space
with Gibbs measures via an SPDE approach
,
(with
Michael RÖCKNER),
Journal of Functional Analysis, volume 242 (2007), no.2, pp. 486518.

Asymptotic
expansions
for the Laplace approximations for Ito
functionals of Brownian rough paths
,
(with
Yuzuru INAHAMA),
Journal of Functional Analysis, volume 243 (2007), no. 1, pp. 270322.

On
asymptotics
of Banach spacevalued Ito functionals
of Brownian rough paths
,
(with
Yuzuru INAHAMA),
Stochastic Analysis and Applications: Proceedings of the Second Abel Symposium (2005)
(F.E. Benth, G. Di Nunno, T. Lindstrom, B. Oksendal and T. Zhang eds),
Abel Symposia, volume 2,
Springer (2007), pp. 415434.

The
LittlewoodPaleyStein inequality for diffusion
processes on general metric spaces
,
(with Tomohiro MIYOKAWA),
Journal of Mathematical Sciences, The University of Tokyo,
volume 14 (2007), no. 1, pp. 130.

On
the Laplacetype asymptotics and the stochastic Taylor
expansion for Ito functionals of Brownian rough paths
,
(with
Yuzuru INAHAMA),
Proceedings of RIMS Workshop on
Stochastic Analysis and Applications,
RIMS Kokyuroku Bessatsu, volume B6 (2008), pp. 139152.

Topics
on diffusion semigroups on a path space with Gibbs measures
,
Proceedings of RIMS Workshop on
Stochastic Analysis and Applications,
RIMS Kokyuroku Bessatsu,
volume B6 (2008), pp. 153165.

Strong
uniqueness
for both Dirichlet operators and
stochastic dynamics to Gibbs measures on a path space
with exponential interactions
,
(with
Sergio ALBEVERIO
and
Michael RÖCKNER),
Journal of Functional Analysis, volume 262 (2012), no. 2, pp. 602638.
(a preliminary version:
available here )

An
explicit effect of nonsymmetry of
random walks on the triangular lattice
,
(with
Satoshi ISHIWATA
and
Tsubasa TERUYA), submitted.
(
available here )
List of
Scientific Talks and Other Documents (Mainly in Japanese)
Lectures (In Japanese)
Okayama Analysis and Probability Seminar
Workshop ``Rough Path Analysis and Related Topics" (Nagoya, January 2012)
International Conference ``Stochastic Analysis and Applications" (Okayama, September 2012)
Links
Return to Department of Mathematics, Okayama University
.