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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

Citations:

Zbl 0635.00012