Euler Scheme for Stochastic Functional Differential Equations Driven by Fractional Brownian Motion via Fractional Calculus Techniques
Provides a numerical method for a class of stochastic differential equations with memory, relevant for researchers in stochastic analysis and computational mathematics.
The paper proposes and analyzes an Euler-type numerical scheme for stochastic functional differential equations driven by fractional Brownian motion with Hurst parameter H>1/2, proving convergence and deriving the rate. Numerical simulations confirm the method's accuracy.
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.