Bayesian inference of discretely observed diffusions

Abstract

We consider the inverse problem of recovering the diffusion and drift functions of a stochastic differential equation from discrete measurements of its solution. We show the stability of the posterior measure with respect to appropriate approximations of the underlying forward model allowing for priors with unbounded support. Motivated by applications in modeling of epidemic processes on networks, we also look at the case where the diffusion coefficient vanishes at a boundary point.

This is based on joint work with J.-C. Croix, S. Katsarakis, I. Kiss and T. Zerenner.