# Research

## Stochastic Modelling

The problems of data assimilation and inverse problems lead naturally to many challenging questions in the area of stochastic modelling. For example random or stochastic differential equations which are invariant with respect to a given probability measure arise in the study of Bayesian inverse problems; the ergodic properties of stochastic dynamical systems, together with properties of the random attractor, characterize data assimilation algorithms. Stuart has research a research program in stochastic modelling, focussed on the study of Monte Carlo Markov Chain algorithms, multiscale problems, the numerical approximation of stochastic processes and stochastic partial differential equations.