Hiroshi KAWABI . .

Position: Associate Professor
Affiliation: Department of Mathematics, Faculty of Science, Okayama University, JAPAN

e-mail: my-family-name AT math.okayama-u.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.))

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, Keio-Shiki 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

• 2003/4-2004/3
  JSPS Research Fellowship (DC2), Graduate School of Mathematical Sciences, The University of Tokyo
  
  
• 2004/4-2006/3
  JSPS Post-Doctral Research Fellowship, Graduate School of Engineering Science, Osaka University
  • 2004/10-2004/12
    Visiting Scholar at Research Center BiBoS, University of Bielefeld,GERMANY
  • 2004/12, 2005/5-2005/8
    Visiting Scholar at Institute for Applied Mathematics, University of Bonn, GERMANY

• 2006/4-2007/3
  COE Post-Doctral Fellow, Faculty of Mathematics, Kyushu University , JAPAN

• 2007/4-
  Associate Professor, Department of Mathematics, Faculty of Science, Okayama University
  • 2010/1-2010/7
    Visiting Member at Isaac Newton Institute for Mathematical Sciences, University of Cambridge, UK
    (Research Programme No.85 : Stochastic Partial Differential Equations (SPD))

Research Papers

1. Short time asymptotics of a certain infinite dimensional diffusion process ,
   (with Shigeki AIDA),
   Stochastic Analysis and Related Topics VII: Proceeding of 7-th Silvri Work-shop
   (L. Decreusefond, B. Oksendal and A. S. Ustunel eds.), Progress in Probability, volume 48,
   Birkhauser (2001), pp. 77--124.
   
   
2. Functional inequalities and an application for parabolic stochastic partial differential equations containing rotation,
   Bulletin des Sciences Mathematiques, volume 128 (2004), no. 8, pp. 687--725.
   
   
3. The parabolic Harnack inequalities for the time dependent Ginzburg-Landau type SPDE and its application ,
   Potential Analysis , volume 22 (2005), no. 1, pp. 61--84.
   
   
4. On a construction of weak solutions to non-stationary Stokes type equations by minimizing variational functionals and their regularity,
   Commentationes Mathematicae Universitatis Carolinae, volume 46 (2005) no. 1, pp. 161--178.
   
   
5. A simple proof of the log-Sobolev inequality on the path space with Gibbs measures,
   Infinite Dimensional Analysis, Quantum Probability and Related Topics (IDAQP) , volume 9 (2006), no. 2, pp. 321--329.
   
   
6. 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. 797--816.
   
   
7. Essential self-adjointness 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. 486--518.
   
   
8. 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. 270--322.
   
   
9. On asymptotics of Banach space-valued 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. 415--434.
   
   
10. The Littlewood-Paley-Stein 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. 1--30.
    
    
11. On the Laplace-type 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. 139--152.
    
    
12. 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. 153--165.
    
    
13. 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. 602--638.
    (a preliminary version: available here )
    
    
14. An explicit effect of non-symmetry of random walks on the triangular lattice ,
    (with Satoshi ISHIWATA and Tsubasa TERUYA), submitted.
    ( available here )
    
    
    

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