Numerical Scheme for Stochastic Differential Equations Driven by Fractional Brownian Motion with 1 / 4 < H< 1 / 2 .

Héctor Araya; Jorge A. León; Soledad Torres

doi:10.1007/s10959-019-00902-3

Numerical Scheme for Stochastic Differential Equations Driven by Fractional Brownian Motion with 1 / 4 < H< 1 / 2 .

Héctor Araya, Jorge A. León, Soledad Torres

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

In this article, we study a numerical scheme for stochastic differential equations driven by fractional Brownian motion with Hurst parameter 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^-²^H⁺^ρ, for ρ small enough.

Original language	English
Pages (from-to)	1211-1237
Number of pages	27
Journal	Journal of Theoretical Probability
Volume	33
Issue number	3
DOIs	https://doi.org/10.1007/s10959-019-00902-3
State	Published - 1 Sep 2020
Externally published	Yes

Keywords

Doss–Sussmann representation
Fractional Brownian motion
Stochastic differential equation
Taylor expansion

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10.1007/s10959-019-00902-3

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title = "Numerical Scheme for Stochastic Differential Equations Driven by Fractional Brownian Motion with 1 / 4 < H< 1 / 2 .",

abstract = "In this article, we study a numerical scheme for stochastic differential equations driven by fractional Brownian motion with Hurst parameter 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+ρ, for ρ small enough.",

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author = "H{\'e}ctor Araya and Le{\'o}n, {Jorge A.} and Soledad Torres",

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AU - Torres, Soledad

PY - 2020/9/1

Y1 - 2020/9/1

N2 - In this article, we study a numerical scheme for stochastic differential equations driven by fractional Brownian motion with Hurst parameter 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+ρ, for ρ small enough.

AB - In this article, we study a numerical scheme for stochastic differential equations driven by fractional Brownian motion with Hurst parameter 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+ρ, for ρ small enough.

KW - Doss–Sussmann representation

KW - Fractional Brownian motion

KW - Stochastic differential equation

KW - Taylor expansion

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ER -

Numerical Scheme for Stochastic Differential Equations Driven by Fractional Brownian Motion with 1 / 4 < H< 1 / 2 .

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Keywords

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