Approximations of fractional stochastic differential equations by means of transport processes

Abstract

We present strong approximations with rate of convergence for the solution of a stochastic differential equation of the formH is fractional Brownian motion with Hurst index H, and we assume existence of a unique solution with Doss-Sussmann representation.The results are based on a strong approximation of B H by means of transport processes of Garzón et al (2009 [11]).If σ is bounded away from 0, an approximation is obtained by a general Lipschitz dependence result of Römisch and Wakolbinger (1985 [25]).Without that assumption on σ, that method does not work, and we proceed by means of Euler schemes on the Doss-Sussmann representation to obtain another approximation, whose proof is the bulk of the paper.

Locations

• Communications on Stochastic Analysis - View - PDF
• arXiv (Cornell University) - View - PDF