## Bernoulli

- Bernoulli
- Volume 25, Number 3 (2019), 2183-2205.

### Consistency of Bayesian nonparametric inference for discretely observed jump diffusions

Jere Koskela, Dario Spanò, and Paul A. Jenkins

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#### Abstract

We introduce verifiable criteria for weak posterior consistency of 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 priors built from discrete nets, wavelet expansions, and Dirichlet mixture models satisfy our conditions. This generalises known results by incorporating jumps into previous work on unit diffusions with uniformly Lipschitz drift coefficients.

#### Article information

**Source**

Bernoulli, Volume 25, Number 3 (2019), 2183-2205.

**Dates**

Received: October 2015

Revised: November 2017

First available in Project Euclid: 12 June 2019

**Permanent link to this document**

https://projecteuclid.org/euclid.bj/1560326442

**Digital Object Identifier**

doi:10.3150/18-BEJ1050

**Mathematical Reviews number (MathSciNet)**

MR3961245

**Zentralblatt MATH identifier**

07066254

**Keywords**

Bayesian statistics Dirichlet mixture model prior discrete net prior jump diffusion nonparametric inference posterior consistency

#### Citation

Koskela, Jere; Spanò, Dario; Jenkins, Paul A. Consistency of Bayesian nonparametric inference for discretely observed jump diffusions. Bernoulli 25 (2019), no. 3, 2183--2205. doi:10.3150/18-BEJ1050. https://projecteuclid.org/euclid.bj/1560326442

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