Stochastic differential equations driven by fractional Brownian motion

TL;DR

This paper analyzes stochastic differential equations driven by fractional Brownian motion with H>0.5, establishing existence and uniqueness of solutions using fractional white noise theory and L^2-estimates.

Contribution

It introduces a new approach to prove existence and uniqueness of solutions for SDEs driven by fractional Brownian motion with H>0.5, based on fractional white noise and L^2-estimates.

Findings

Proves a fundamental L^2-estimate for WIS-integrals.

Establishes existence and uniqueness of solutions under Lipschitz conditions.

Summarizes fractional white noise theory relevant to the analysis.

Abstract

The aim of this paper is to analyse a WIS-stochastic differential equation driven by fractional Brownian motion with H>0.5. For this, we summarise the theory of fractional white noise and prove a fundamental L^2-estimate for WIS-integrals. We apply this to prove the existence and uniqueness of a solution in L^2(P) of a WIS-stochastic differential equation driven fractional Brownian motion with H>0.5 under Lipschitz conditions on its coefficients.