Quasi-likelihood analysis for the stochastic differential equation with jumps

In this paper, we consider a multidimensional diffusion process X with jumps whose jump term is driven by a compound Poisson process, and discuss its parametric estimation. We present asymptotic normality and convergence of moments of any order for a quasi-maximum likelihood estimator and a Bayes type estimator by assuming an exponential mixing property of X. To show these properties, we use the polynomial type large deviation theory.