Consistency of Bayesian nonparametric inference for discretely observed jump diffusions

摘要

We introduce verifiable criteria for weak posterior consistency ofidentifiable Bayesian nonparametric inference for jump diffusions with unitdiffusion coefficient and uniformly Lipschitz drift and jump coefficients inarbitrary dimension. The criteria are expressed in terms of coefficients of theSDEs describing the process, and do not depend on intractable quantities suchas transition densities. We also show that products of discrete net andDirichlet mixture model priors satisfy our conditions, again under anidentifiability assumption. This generalises known results by incorporatingjumps into previous work on unit diffusions with uniformly Lipschitz driftcoefficients.