Analysis of an approximation scheme for stationary distributions of stochastic differential equations.

Abstract:

The most natural way to approximate the stationary distribution of an ergodic SDE is to discretize it and look at the empirical average. The discretization introduces an error which we will argue cannot be easily quantified in this infinite time horizon problem. However very little is available on mathematical analyses of numerical schemes in this context. This is in contrast to the situation where discretization schemes are used to approximate trajectories of an SDE over fixed finite interval, and where the research on error analysis is  of course abundant. In this talk, we will discuss how the discretization step can be properly scaled to achieve functional CLT for the error term and even exponential decay of error probabilities.  This is a joint work with P. Sundar.