Stochastic evolution equations with random generators

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Issue Date
1998-05-01Author
Leon, Jorge A.
Nualart, David
Publisher
Institute of Mathematical Statistics (IMS)
Type
Article
Article Version
Scholarly/refereed, publisher version
Metadata
Show full item recordAbstract
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.
Description
This is the published version, also available here: http://dx.doi.org/10.1214/aop/1022855415.
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Citation
Le{\'o}n, Jorge A.; Nualart, David. Stochastic evolution equations with random generators. Ann. Probab. 26 (1998), no. 1, 149--186. http://dx.doi.org/10.1214/aop/1022855415.
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