TITLE: On the complexity of strong approximation of SDEs with a non-Lipschitz drift coefficient

ABSTRACT: We study pathwise approximation of stochastic differential equations (SDEs) at a single time based on finitely many (sequential) evaluations of the driving Brownian motion. The classical assumption in the literature on numerical approximation of SDEs is global Lipschitz continuity of the coefficients of the equation. However, many SDEs arising in applications fail to have globally Lipschitz continuous coefficients. In this talk we focus on the case when the drift coefficient is not Lipschitz continuous.
In particular, we discuss recent results on corresponding upper and lower error bounds for SDEs with a discontinuous or H¨older continuous drift coefficient. The talk is based on joint work with Simon Ellinger (University of Passau), Arnulf Jentzen (Univerity of M¨unster) and Thomas M¨uller-Gronbach (University of Passau).