Articlegreen2017

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

35 citations0/0 files storedIMA Journal of Numerical Analysis

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Stochastic processes and financial applications Advanced Numerical Methods in Computational Mathematics Fractional Differential Equations Solutions

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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1968Fractional Brownian Motions, Fractional Noises and Applications 1999Essentials of Stochastic Finance 2000ESSENTIALS OF STOCHASTIC FINANCE 2003Measuring anti-correlations in the nordic electricity spot market by wavelets 2006On numerical solution of stochastic partial differential equations of elliptic type

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2020Optimal rate of convergence for two classes of schemes to stochastic differential equations driven by fractional Brownian motions

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