Probablistic Methods for Higher-order Weak Approximation of Stochastic Differential Equations

Abstract

Numerical calculation of E[f(X(1,x))] where {X(t,x)}_t≧0 is a diffusion process defined by a stochastic differential equation (SDE) is called weak approximation of the SDE. The author discusses higherorder discretization algorithms based on Kusuokaʼs theory. The fundamental theorem by Kusuoka and three algorithms are explained.