Weak approximation of a fractional SDE

TL;DR

This paper demonstrates a diffusion approximation for fractional SDEs driven by fractional Brownian motion with Hurst parameter between 1/3 and 1/2, using algebraic integration and Poisson process approximations.

Contribution

It introduces a new approximation method for fractional SDEs leveraging algebraic integration and Poisson process techniques.

Findings

Validates the diffusion approximation for fractional SDEs with H in (1/3,1/2)

Extends previous approximation methods to fractional Brownian motion

Uses algebraic integration theory for rigorous proof

Abstract

In this note, a diffusion approximation result is shown for stochastic differential equations driven by a (Liouville) fractional Brownian motion B with Hurst parameter H in (1/3,1/2). More precisely, we resort to the Kac-Stroock type approximation using a Poisson process studied in Bardina, Jolis and Tudor (2003) and Delgado and Jolis (2000), and our method of proof relies on the algebraic integration theory introduced by Gubinelli (2004).