A type of Gauss’ divergence formula on Wiener spaces. (English) Zbl 1189.60112

Otobe, Yoshiki

Electron. Commun. Probab. 14, 457-463 (2009).

Summary: We will formulate a type of Gauss’ divergence formula on sets of functions which are greater than a specific value of which boundaries are not regular. Such formula was first established by L. Zambotti in [Probab. Theory Relat. Fields 123, No. 4, 579–600 (2002; Zbl 1009.60047)] with a profound study of stochastic processes. In this paper we will give a much shorter and simpler proof for his formula in a framework of the Malliavin calculus and give alternate expressions. Our approach also enables to show that such formulae hold in other Gaussian spaces.

MSC:

60H07	Stochastic calculus of variations and the Malliavin calculus
28C20	Set functions and measures and integrals in infinite-dimensional spaces (Wiener measure, Gaussian measure, etc.)

Keywords:

divergence formulae on the Wiener spaces; integration by parts formulae on the Wiener spaces

Citations:

Zbl 1009.60047