Journal
JOURNAL OF DIFFERENTIAL EQUATIONS
Volume 266, Issue 8, Pages 4568-4623Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jde.2018.10.008
Keywords
Wong-Zakai approximation; Stochastic evolution equation; Multiplicative noise; Invariant manifolds; Invariant foliations
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Funding
- NSFC [11501549, 11331007]
- NSF [1413603]
- Fundamental Research Funds for the Central Universities [YJ201646]
- Direct For Mathematical & Physical Scien
- Division Of Mathematical Sciences [1413603] Funding Source: National Science Foundation
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In this paper, we study the Wong-Zakai approximations given by a stationary process via the Wiener shift and their associated dynamics of a class of stochastic evolution equations with a multiplicative white noise. We prove that the solutions of Wong-Zakai approximations almost surely converge to the solutions of the Stratonovich stochastic evolution equation. We also show that the invariant manifolds and stable foliations of the Wong-Zakai approximations converge to the invariant manifolds and stable foliations of the Stratonovich stochastic evolution equation, respectively. (C) 2018 Elsevier Inc. All rights reserved.
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