Euler scheme for stochastic functional differential equations driven by fractional Brownian motion
Year: 2026
Type: preprint
Abstract: 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.
Source: arXiv (Cornell University)
Authors: Garzón, Johanna, León, Jorge A., Lozada, Jorge, Torres, Soledad
Subfield: Finance
Domain: Social Sciences
Open Access status: green
OpenAlex ID: W7148988610
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