On strong approximation of SDEs with a discontinuous drift coefficient

Larisa Yaroslavtseva (University of Graz) will talk about:

The classical assumption in the literature on numerical approximation of stochastic differential equations (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 the last decade an intensive study of numerical approximation of SDEs with non-globally Lipschitz continuous coefficients has begun. In particular, strong approximation of   SDEs  with a drift coefficient that is discontinuous in space has recently gained a lot of interest. Such SDEs arise e.g. in mathematical finance, insurance  and stochastic control problems. Classical techniques of error analysis are not  applicable to such SDEs and well known convergence results for standard methods do not carry over in general. 

In this talk I will present   recent results on strong approximation of such SDEs.  

The talk is based on joint work with Arnulf Jentzen (University of Münster) and Thomas Müller-Gronbach (University of Passau).