Strong convergence of a fully discrete scheme for stochastic Burgers equation with fractional-type noise
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866914487032872960 |
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| author | Wang, Yibo Cao, Wanrong |
| author_facet | Wang, Yibo Cao, Wanrong |
| contents | We investigate numerical approximations for the stochastic Burgers equation driven by an additive cylindrical fractional Brownian motion with Hurst parameter $H \in (\frac{1}{2}, 1)$. To discretize the continuous problem in space, a spectral Galerkin method is employed, followed by the presentation of a nonlinear-tamed accelerated exponential Euler method to yield a fully discrete scheme. By showing the exponential integrability of the stochastic convolution of the fractional Brownian motion, we present the boundedness of moments of semi-discrete and full-discrete approximations. Building upon these results and the convergence of the fully discrete scheme in probability proved by a stopping time technique, we derive the strong convergence of the proposed scheme. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_00951 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Strong convergence of a fully discrete scheme for stochastic Burgers equation with fractional-type noise Wang, Yibo Cao, Wanrong Numerical Analysis Probability 60H35, 65C30, 60H15 We investigate numerical approximations for the stochastic Burgers equation driven by an additive cylindrical fractional Brownian motion with Hurst parameter $H \in (\frac{1}{2}, 1)$. To discretize the continuous problem in space, a spectral Galerkin method is employed, followed by the presentation of a nonlinear-tamed accelerated exponential Euler method to yield a fully discrete scheme. By showing the exponential integrability of the stochastic convolution of the fractional Brownian motion, we present the boundedness of moments of semi-discrete and full-discrete approximations. Building upon these results and the convergence of the fully discrete scheme in probability proved by a stopping time technique, we derive the strong convergence of the proposed scheme. |
| title | Strong convergence of a fully discrete scheme for stochastic Burgers equation with fractional-type noise |
| topic | Numerical Analysis Probability 60H35, 65C30, 60H15 |
| url | https://arxiv.org/abs/2408.00951 |