The Annals of Probability

Stochastic evolution equations with random generators

Jorge A. Le{\'o}n and David Nualart

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Abstract

We prove the existence of a unique mild solution for a stochastic evolution equation on a Hilbert space driven by a cylindrical Wiener process. The generator of the corresponding evolution system is supposed to be random and adapted to the filtration generated by the Wiener process. The proof is based on a maximal inequality for the Skorohod integral deduced from the Itô’s formula for this anticipating stochastic integral.

Article information

Source
Ann. Probab., Volume 26, Number 1 (1998), 149-186.

Dates
First available in Project Euclid: 31 May 2002

Permanent link to this document
https://projecteuclid.org/euclid.aop/1022855415

Digital Object Identifier
doi:10.1214/aop/1022855415

Mathematical Reviews number (MathSciNet)
MR1617045

Zentralblatt MATH identifier
0939.60066

Subjects
Primary: 60H15: Stochastic partial differential equations [See also 35R60] 60H07: Stochastic calculus of variations and the Malliavin calculus

Keywords
Stochastic evolution equations stochastic anticipating calculus Skorohod integral

Citation

Le{\'o}n, Jorge A.; Nualart, David. Stochastic evolution equations with random generators. Ann. Probab. 26 (1998), no. 1, 149--186. doi:10.1214/aop/1022855415. https://projecteuclid.org/euclid.aop/1022855415


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