Time-Stepping Error Bound for a Stochastic Parabolic Volterra Equation Disturbed by Fractional Brownian Motions
Year: 2019
Numerical Mathematics: Theory, Methods and Applications, Vol. 12 (2019), Iss. 3 : pp. 778–796
Abstract
In this paper, we consider a stochastic parabolic Volterra equation driven by the infinite dimensional fractional Brownian motion with Hurst parameter $H$ ∈ [$\frac{1}{2}$,1). We apply the piecewise constant, discontinuous Galerkin method to discretize this equation in the temporal direction. Based on the explicit form of the scalar resolvent function and the refined estimates for the Mittag-Leffler function, we derive sharp mean-square regularity results for the mild solution. The sharp regularity results enable us to obtain the optimal error bound of the time discretization. These theoretical findings are finally accompanied by several numerical examples.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/ 10.4208/nmtma.OA-2017-0153
Numerical Mathematics: Theory, Methods and Applications, Vol. 12 (2019), Iss. 3 : pp. 778–796
Published online: 2019-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 19
Keywords: Stochastic parabolic Volterra equation fractional Brownian motion optimal error bound.