Numerical Scheme for Stochastic Differential Equations Driven by Fractional Brownian Motion with $$ 1/4

Héctor Araya (), Jorge A. León () and Soledad Torres ()
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Héctor Araya: Universidad de Valparaíso
Jorge A. León: Cinvestav-IPN
Soledad Torres: Universidad de Valparaíso

Journal of Theoretical Probability, 2020, vol. 33, issue 3, 1211-1237

Abstract: Abstract In this article, we study a numerical scheme for stochastic differential equations driven by fractional Brownian motion with Hurst parameter $$ H \in \left( 1/4, 1/2 \right) $$ H ∈ 1 / 4 , 1 / 2 . Toward this end, we apply Doss–Sussmann representation of the solution and an approximation of this representation using a first-order Taylor expansion. The obtained rate of convergence is $$n^{-2H +\rho }$$ n - 2 H + ρ , for $$\rho $$ ρ small enough.

Keywords: Doss–Sussmann representation; Fractional Brownian motion; Stochastic differential equation; Taylor expansion (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s10959-019-00902-3

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