Abstract
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.
| Original language | English |
|---|---|
| Pages (from-to) | 1958-1981 |
| Number of pages | 24 |
| Journal | SIAM Journal on Numerical Analysis |
| Volume | 55 |
| Issue number | 4 |
| DOIs | |
| Publication status | Published - 2017 |
| Externally published | Yes |
Bibliographical note
Publisher Copyright:© 2017 Society for Industrial and Applied Mathematics.
Keywords
- Fractional Brownian motion
- Galerkin approximation
- Stochastic evolution equation
- Wong-Zakai approximation
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