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January 1998 Stochastic evolution equations with random generators
Jorge A. Le{\'o}n, David Nualart
Ann. Probab. 26(1): 149-186 (January 1998). DOI: 10.1214/aop/1022855415


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.


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Jorge A. Le{\'o}n. David Nualart. "Stochastic evolution equations with random generators." Ann. Probab. 26 (1) 149 - 186, January 1998.


Published: January 1998
First available in Project Euclid: 31 May 2002

zbMATH: 0939.60066
MathSciNet: MR1617045
Digital Object Identifier: 10.1214/aop/1022855415

Primary: 60H07 , 60H15

Keywords: Skorohod integral , stochastic anticipating calculus , stochastic evolution equations

Rights: Copyright © 1998 Institute of Mathematical Statistics

Vol.26 • No. 1 • January 1998
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