On long time approximation of ergodic stochastic differential equations
In this talk we will discuss a variety of different problems related to the long time behaviour of solutions of stochastic differential equations (SDEs). This is an important question with relevance in many field of applied mathematics and statistics. Once the limiting behaviour of the SDE has been established, one needs to design appropriate numerical algorithms that are able to capture it correctly.
This is a very delicate problem and to address this we will present a general framework based on recent developments in backward error analysis for SDEs . Using the underlying methodology we will then analyze stochastic algorithms arising in molecular dynamics as well as machine learning.