Special Session 153: Stochastic computing and structure preserving methods

Old and new numerical methods for SPDEs: non-asymptotic uniform in time error bounds
Michela Ottobre
Heriot Watt University and Maxwell Institute, Edinburgh
Scotland
Co-Author(s):    Can Huang, Gideon Simpson
Abstract:
We discuss numerical methods to sample from the invariant measure of a class of SPDEs with non-Lipshitz drift, focusing in particular on tamed schemes. The methods we present approximate the SPDE dynamics uniformly in time; that is, they approximate correctly both the transient and the long time behaviour. We will show this fact by providing bounds which are non-asymptotic. Moreover, we will discuss a general approach to prove non-asymptotic, uniform in time bounds for approximations of Markovian dynamics. This approach has been shown to work for a range of Markovian dynamics and associated approximations( whether the approximation is produced numerically, via particle systems or via other methods).