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Stochastic evolution equations with random generators

Leon, Jorge A.
; 
Nualart, David
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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.
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This is the published version, also available here: http://dx.doi.org/10.1214/aop/1022855415.
Date
1998-05-01
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Institute of Mathematical Statistics (IMS)
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Mathematics Scholarly Works
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NualartD_AP_26(1)149.pdf
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Keywords
Stochastic evolution equations, Skorohod integral, stochastic anticipating calculus
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.
URI
https://hdl.handle.net/1808/17054
DOI
10.1214/aop/1022855415
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