Stochastic Analysis Seminar – G.J. Lord (Gabriel) (Radboud University)

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). 

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 for  H > 0.5. 

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 of   min(H+0.5,1). 

 This is joint with with Roy Schieven and Utku Erdogan.