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arXiv · 1507.02399

Finite element approximations for second order stochastic differential equation driven by fractional Brownian motion

Yanzhao Cao·Jialin Hong·Zhihui Liu
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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 $H\le 1/2$. 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.

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Yanzhao Cao, Jialin Hong, Zhihui Liu. 2015-07-09. Finite element approximations for second order stochastic differential equation driven by fractional Brownian motion. https://doi.org/10.1093/imanum%2Fdrx004

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