On the global Lipschitz assumption in computational stochastics

Arnulf Jentzen, Uni Bielefeld

Abstract: Stochastic differential equations are often simulated with the Monte Carlo Euler method. Convergence of this method is well understood in the case of globally Lipschitz continuous coefficients of the stochastic differential equation. The important case of superlinearly
growing coefficients, however, remained an open question for a long time now. In this talk we answer this question and establish convergence of the Monte Carlo Euler method for a large class of stochastic differential equations whose drift functions have at most polynomial growth.