Short time asymptotics for fundamental solutions of diffusion equations. (English) Zbl 0647.60085

Ikeda, Nobuyuki; Kusuoka, Shigeo

Stochastic analysis, Proc. Jap.-Fr. Semin., Paris/France 1987, Lect. Notes Math. 1322, 37-49 (1988).

[For the entire collection see Zbl 0635.00012.]
The asymptotic behaviour of the reflecting Brownian motion in the exterior of a strictly convex domain with smooth boundary is studied. The formula \[ \ell n p(t,x,y)=-\rho (x,y)^ 2/(2t)-C/(2t)^{1/3}+o(t^{- 1/3}),\quad t\downarrow 0, \] is proved for a domain of general type, where C depends on the boundary. The proof is based on generalized Malliavin calculus.

Reviewer: A.Yu.Veretennikov

MSC:

60J60	Diffusion processes
60J35	Transition functions, generators and resolvents
60F10	Large deviations
60H15	Stochastic partial differential equations (aspects of stochastic analysis)
60J65	Brownian motion

Keywords:

asymptotic behaviour; reflecting Brownian motion; strictly convex domain; generalized Malliavin calculus

Citations:

Zbl 0635.00012