Journal
SIAM JOURNAL ON NUMERICAL ANALYSIS
Volume 55, Issue 4, Pages 1958-1981Publisher
SIAM PUBLICATIONS
DOI: 10.1137/16M1056122
Keywords
stochastic evolution equation; fractional Brownian motion; Wong-Zakai approximation; Galerkin approximation
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Funding
- National Natural Science Foundation of China [91630312, 91530118, 11290142]
- U.S. National Science Foundation [DMS1620150]
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In this paper, we analyze Galerkin approximations for stochastic evolution equations driven by an additive Gaussian noise which is temporally white and spatially fractional with Hurst index less than or equal to 1/2. First we regularize the noise by the Wong-Zakai approximation and obtain its optimal order of convergence. Then we apply the Galerkin method to discretize the stochastic evolution equations with regularized noises. Optimal error estimates are obtained for the Galerkin approximations. In particular, our error estimates remove an infinitesimal factor which appears in the error estimates of various numerical methods for stochastic evolution equations in existing literatures.
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