Current Affiliation Organization 【 display / non-display 】

Current Affiliation Organization 【 display / non-display 】

Academic degree 【 display / non-display 】

Academic degree 【 display / non-display 】

External Career 【 display / non-display 】

External Career 【 display / non-display 】

Research Interests 【 display / non-display 】

Research Interests 【 display / non-display 】

Research Areas 【 display / non-display 】

Research Areas 【 display / non-display 】

Published Papers 【 display / non-display 】

Published Papers 【 display / non-display 】

• Asymptotic behaviors on the small parameter exit problems and the singularly perturbation problems

  その他の著者

  Vol.14 (2001) ( Department of Mathematical Sciences, Faculty of Science, University of the Ryukyus )  14   79 - 118   2010.01

  Type of publication: Research paper (bulletin of university, research institution)

  　View Summary

  We consider the small parameter exit problems for diffusion processes and the associated singular perturbed Dirichlet problems. We investigate the asymptotic relations between the mean exit time and the principal eigenvalue. Two problems are considered under the gradient condition for the corresponding dynamical system. One is under the uniqueness of deepest valley, where we show that the product of the mean exit time and the principal eigenvalue converges to one exponentially fast. The other is related to the sharp asymptotics of the mean exit times, the eigenvalues and eigenfunctions, where we characterize the scaling limits of them by the Markov chain which appears metastable behavior of the corresponding diffusion process. To do this, we extend the methods used in our previous papers [10] and [11]. （管理者追加）リポジトリ登録情報を移行しました。確認のうえ、加除修正をしてください。

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Grant-in-Aid for Scientific Research 【 display / non-display 】

Grant-in-Aid for Scientific Research 【 display / non-display 】

• Stochastic analysis on large scale interacting systems and its applications

  Grant-in-Aid for Scientific Research(A)

  Project Year: 2010.04  -  2015.03 

  Investigator(s): FUNAKI Tadahisa, OSADA Hirofumi, MATANO Hiroshi, HIGUCHI Yasunari, OTOBE Yoshiki, TANEMURA Hideki, CHIYONOBU Taizo, KUMAGAI Takashi, HANDA Kenji, YOSHIDA Nobuo, SUGIURA Makoto, ICHIHARA Naoyuki, NISHIKAWA Takao, SAKAGAWA Hironobu, XIE Bin 

  Direct: 32,100,000 (YEN)  Overheads: 41,730,000 (YEN)  Total: 9,630,000 (YEN)

  　View Summary

  We studied invariant measures of KPZ equation which describes a growth of interfaces with fluctuations. This stochastic partial differential equation involves a diverging term which makes difficult to give a mathematical meaning to it. We discussed the non-equilibrium fluctuation problem for the dynamics of two-dimensional Young diagrams and derived a stochastic partial differential equation under a scaling limit. The method of the hydrodynamic limit is applied to a system of creatures with an effect of self-organized aggregation and established a link between macroscopic and microscopic descriptions. We proved unique existence of strong solutions of infinite dimensional stochastic differential equations and rigidity for Airy point process and Ginibre point process, which appear in the theory of dynamic random matrices. Furthermore, we studied percolations, nonlinear diffusion equations, stochastic partial differential equations with stable noises and others.

• Grant-in-Aid for Young Scientists(B)

  Project Year: 2003  -  2005 

  Direct: 1,200,000 (YEN)  Total: 1,200,000 (YEN)

• Grant-in-Aid for Scientific Research(C)

  Project Year: 1999.04  -  2001.03 

  Direct: 1,500,000 (YEN)  Overheads: 450,000 (YEN)  Total: 1,950,000 (YEN)