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Strong convergence of a fully discrete scheme for stochastic Burgers equation with fractional-type noise
- Publication Year :
- 2024
-
Abstract
- 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.<br />Comment: 23 pages
- Subjects :
- Mathematics - Numerical Analysis
Mathematics - Probability
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2408.00951
- Document Type :
- Working Paper