TY - JOUR
T1 - Time-Stepping Error Bound for a Stochastic Parabolic Volterra Equation Disturbed by Fractional Brownian Motions
JO - Numerical Mathematics: Theory, Methods and Applications
VL - 3
SP - 778
EP - 796
PY - 2019
DA - 2019/04
SN - 12
DO - http://doi.org/ 10.4208/nmtma.OA-2017-0153
UR - https://global-sci.org/intro/article_detail/nmtma/13130.html
KW - Stochastic parabolic Volterra equation, fractional Brownian motion, optimal error
bound.
AB - <p style="text-align: justify;">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.</p>