Euler Scheme for Stochastic Functional Differential Equations Driven by Fractional Brownian Motion via Fractional Calculus Techniques

Alexander Abreu, Héctor Araya, Lisandro Fermin (), Johanna Garzón and Soledad Torres
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Alexander Abreu: CIMFAV - Centro de Investigación y Modelamiento de Fenómenos Aleatorios – Valparaíso - Universidad de Valparaiso = Valparaiso University
Héctor Araya: UNAI - Faculty of Engineering \& Sciences - UAI - Unione Astrofili Italiani
Lisandro Fermin: AMSE - Aix-Marseille Sciences Economiques - EHESS - École des hautes études en sciences sociales - AMU - Aix Marseille Université - ECM - École Centrale de Marseille - CNRS - Centre National de la Recherche Scientifique
Johanna Garzón: UNAL - Departamento de Matemáticas - UNAL - Universidad Nacional de Colombia [Bogotà]
Soledad Torres: CIMFAV - Centro de Investigación y Modelamiento de Fenómenos Aleatorios – Valparaíso - Universidad de Valparaiso = Valparaiso University

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Abstract: We study a stochastic functional differential equation (SFDE) with memory driven by a fractional Brownian motion (fBm) with Hurst parameter H > 1/2. An Euler-type numerical scheme is proposed and analyzed under suitable regularity conditions on the drift and diffusion coefficients using tools from fractional calculus. We prove the convergence of the scheme and derive the corresponding rate in terms of the discretization step. Numerical simulations illustrate the theoretical results and confirm the accuracy of the proposed method.

Keywords: Euler-Maruyama method; fractional Brownian motion; stochastic functional differential equations; generalized Riemann–Stieltjes integral (search for similar items in EconPapers)
Date: 2026-09-22
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