Consistency of Bayesian nonparametric inference for discretely observed 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.

20 pages

References in corpus (9)

• Convergence rates of posterior distributions for noniid observations
• Equivalent and absolutely continuous measure changes for jump-diffusion processes
• Penalized nonparametric mean square estimation of the coefficients of diffusion processes
• A modified lookdown construction for the Xi-Fleming-Viot process with mutation and populations with recurrent bottlenecks
• Nonparametric Bayesian posterior contraction rates for discretely observed scalar diffusions
• Reversible jump MCMC for nonparametric drift estimation for diffusion processes
• Consistent nonparametric Bayesian inference for discretely observed scalar diffusions
• On the exact and $\epsilon$-strong simulation of (jump) diffusions
• Non-parametric Bayesian drift estimation for stochastic differential equations

Cited by in corpus (3)

• Nonparametric Bayesian posterior contraction rates for discretely observed scalar diffusions
• Bayesian non-parametric inference for $\Lambda$-coalescents: consistency and a parametric method
• Nonparametric Bayesian volatility estimation for gamma-driven stochastic differential equations