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

Producción científica: Contribución a una revista › Artículo › revisión exhaustiva

6 Citas (Scopus)

Resumen

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.

Idioma original	Inglés
Páginas (desde-hasta)	1211-1237
Número de páginas	27
Publicación	Journal of Theoretical Probability
Volumen	33
N.º	3
DOI	https://doi.org/10.1007/s10959-019-00902-3
Estado	Publicada - 1 sept 2020
Publicado de forma externa	Sí

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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.",

keywords = "Doss–Sussmann representation, Fractional Brownian motion, Stochastic differential equation, Taylor expansion",

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

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AU - León, Jorge A.

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

UR - https://www.scopus.com/pages/publications/85065039201

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

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