Euler scheme for stochastic functional differential equations driven by fractional Brownian motion

Fuente: arXiv
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Main Authors: Garzón, Johanna, León, Jorge A., Lozada, Jorge, Torres, Soledad
Format: Preprint
Published: 2026
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_version_ 1866917378602827776
author Garzón, Johanna
León, Jorge A.
Lozada, Jorge
Torres, Soledad
author_facet Garzón, Johanna
León, Jorge A.
Lozada, Jorge
Torres, Soledad
contents In this paper, we apply rough paths techniques to provide an approximation of the solution of stochastic functional differential equations driven by fractional Brownian motion with Hurst parameter $H>1/2$. Here, the involved stochastic integral is the Young one and the coefficient is evaluated in the set of $λ$-Hölder continuous functions on $[-τ,0]$, for some suitable $τ>0$ and $λ\in(1/2,H)$. The rate of convergence of our scheme is $1/n^γ$, for any $γ<2λ-1$. Also, numerical simulations are provided to illustrate our theoretical results.
format Preprint
id arxiv_https___arxiv_org_abs_2604_01336
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Euler scheme for stochastic functional differential equations driven by fractional Brownian motion
Garzón, Johanna
León, Jorge A.
Lozada, Jorge
Torres, Soledad
Probability
34K07, 65C30
In this paper, we apply rough paths techniques to provide an approximation of the solution of stochastic functional differential equations driven by fractional Brownian motion with Hurst parameter $H>1/2$. Here, the involved stochastic integral is the Young one and the coefficient is evaluated in the set of $λ$-Hölder continuous functions on $[-τ,0]$, for some suitable $τ>0$ and $λ\in(1/2,H)$. The rate of convergence of our scheme is $1/n^γ$, for any $γ<2λ-1$. Also, numerical simulations are provided to illustrate our theoretical results.
title Euler scheme for stochastic functional differential equations driven by fractional Brownian motion
topic Probability
34K07, 65C30
url https://arxiv.org/abs/2604.01336