Régularité \(C^{\infty}\) des noyaux de Wiener d’une diffusion. \((C^{\infty}\)-regularity of Wiener kernels of a diffusion). (French) Zbl 0701.60052

Bernard, Pierre; Nualart, David

Ann. Inst. Henri Poincaré, Probab. Stat. 26, No. 2, 287-297 (1990).

A class of regular Brownian semimartingales is introduced and it is proved that the kernel of the n-th term Wiener chaos decomposition admits a \(C^{\infty}\)-version. It is shown that every diffusion process defined by a stochastic differential equation with \(C_ b^{\infty}\) coefficients belongs to the introduced class and consequently has a regular Wiener kernel.

Reviewer: F.Liese

MSC:

60H07	Stochastic calculus of variations and the Malliavin calculus
60H10	Stochastic ordinary differential equations (aspects of stochastic analysis)

Keywords:

Wiener chaos decomposition; diffusion process; regular Wiener kernel