G.J. Lord (Gabriel)
Title: A numerical method for an SDE with a WIS Integral
Abstract
We examine the numerical approximation of a quasilinear stochastic differential equation (SDE) with multiplicative fractional Brownian motion. The stochastic integral is interpreted in the Wick-Ito-Skorohod (WIS) sense that is well defined and centered for all H in (0,1).Ìý
We give an introduction to the theory of WIS integration before we examine existence and uniqueness of a solution to the SDE. We then introduce our numerical method which is based on the theoretical results in the works of Mishura 2008 forÌý H > 0.5.Ìý
We prove a strong convergence result with rate H. We present some numerical experiments and conjecture that the theoretical results are not optimal since we observe numerically a rate ofÌý Ìýmin(H+0.5,1).Ìý
ÌýThis is joint with with Roy Schieven and Utku Erdogan.