Electronic Communications in Probability

A type of Gauss' divergence formula on Wiener spaces

Yoshiki Otobe

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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 2002 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.

Article information

Electron. Commun. Probab., Volume 14 (2009), paper no. 44, 457-463.

Accepted: 30 October 2009
First available in Project Euclid: 6 June 2016

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Zentralblatt MATH identifier

Primary: 60H07: Stochastic calculus of variations and the Malliavin calculus
Secondary: 28C20: Set functions and measures and integrals in infinite-dimensional spaces (Wiener measure, Gaussian measure, etc.) [See also 46G12, 58C35, 58D20, 60B11]

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

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Otobe, Yoshiki. A type of Gauss' divergence formula on Wiener spaces. Electron. Commun. Probab. 14 (2009), paper no. 44, 457--463. doi:10.1214/ECP.v14-1498. https://projecteuclid.org/euclid.ecp/1465234753

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