Strong convergence of a fully discrete scheme for stochastic Burgers equation with fractional-type noise
<|reference_start|>Strong convergence of a fully discrete scheme for stochastic Burgers equation with fractional-type noise: 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.<|reference_end|>
@article{wang2024strong,
    title={Strong convergence of a fully discrete scheme for stochastic Burgers
  equation with fractional-type noise},
    author={Yibo Wang and Wanrong Cao},
    journal={arXiv preprint arXiv:2408.00951},
    year={2024},
    archivePrefix={arXiv},
    eprint={2408.00951},
    primaryClass={math.NA cs.NA math.PR}
}