Adaptive Bayes estimator for stochastic differential equations with jumps under small noise asymptotics

TL;DR

This paper develops adaptive Bayesian estimators for parameters in stochastic differential equations with jumps, demonstrating their consistency and asymptotic normality under small noise conditions.

Contribution

It introduces a novel adaptive Bayesian estimation method for SDEs with jumps, accounting for multiple unknown parameters and proving their asymptotic properties.

Findings

Estimators are consistent under small noise asymptotics.

Estimators are asymptotically normal.

Method effectively estimates jump-related parameters.

Abstract

In this paper, we consider parameter estimation for stochastic differential equations driven by Wiener processes and compound Poisson processes. We assume unknown parameters corresponding to coefficients of the drift term, diffusion term, and jump term, as well as the Poisson intensity and the probability density function of the underlying jump. We propose estimators based on adaptive Bayesian estimation from discrete observations. We demonstrate the consistency and asymptotic normality of the estimators within the framework of small noise asymptotics.