Consistency of Bayesian nonparametric inference for discretely observed jump diffusions

TL;DR

This paper establishes verifiable conditions for the weak posterior consistency of Bayesian nonparametric inference in jump diffusions, extending previous results to include jump processes with Lipschitz coefficients.

Contribution

It provides new criteria for posterior consistency that depend only on SDE coefficients, applicable to jump diffusions, and demonstrates these with specific prior models.

Findings

Criteria depend only on SDE coefficients, not transition densities

Products of discrete net and Dirichlet mixture priors satisfy the conditions

Generalizes previous diffusion results to jump diffusions

Abstract

We introduce verifiable criteria for weak posterior consistency of identifiable Bayesian nonparametric inference for jump diffusions with unit diffusion coefficient and uniformly Lipschitz drift and jump coefficients in arbitrary dimension. The criteria are expressed in terms of coefficients of the SDEs describing the process, and do not depend on intractable quantities such as transition densities. We also show that products of discrete net and Dirichlet mixture model priors satisfy our conditions, again under an identifiability assumption. This generalises known results by incorporating jumps into previous work on unit diffusions with uniformly Lipschitz drift coefficients.