Finite element approximations for second order stochastic differential equation driven by fractional Brownian motion
Abstract
We consider finite element approximations for a one dimensional second order stochastic differential equation of boundary value type driven by a fractional Brownian motion with Hurst index . We make use of a sequence of approximate solutions with the fractional noise replaced by its piecewise con- stant approximations to construct the finite element approximations for the equation. The error estimate of the approximations is derived through rigorous convergence analysis.
Cite
@article{arxiv.1507.02399,
title = {Finite element approximations for second order stochastic differential equation driven by fractional Brownian motion},
author = {Yanzhao Cao and Jialin Hong and Zhihui Liu},
journal= {arXiv preprint arXiv:1507.02399},
year = {2020}
}
Comments
To appear in IMA Journal of Numerical Analysis; the time-dependent case such as stochastic heat equation and stochastic wave equation driven by fractional Brownian sheet with temporal Hurst index $1/2$ and spatial Hurst index $H\le 1/2$ has been considered by arXiv:1601.02085 for spatially Galerkin approximations and a forthcoming paper for fully discrete approximations