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

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

Zbl 0635.00012