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

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.