Special Session 80: Theory, numerical methods, and applications of stochastic systems and SDEs/SPDEs
Contents
The purpose of this talk is to present a new modified Euler scheme for stochastic differential equations driven by a fractional Brownian motion with Hurst parameter $H>\frac 12$. The rate of convergence of this numerical scheme with step size $1/n$ turns out to be $n^{ \frac12-H}$ if $H\frac 34$.
These results have been obtained applying techniques of Malliavin calculus. We will also discuss the corresponding weak approximation results and central limit theorems for the fluctuations of the approximation error.