Law of large numbers and central limit theorem for a class of pure jump Markov process

This paper studies the law of large numbers (LLN) and central limit theorem (TCL) for a class of scaled pure jump Markov processes where the processes state variables are in R-d and where jump amplitudes depend on the state variables. Non-explosion property and semi-martingale decomposition are studied first for a class of stochastic processes, allowing to study in a second step these same properties for the scaled pure jump Markov processes we consider characterized by infinitely small jumps and rapid jumps rates. Then, asymptotic behavior is derived and convergence results are obtained. (C) 2020 Elsevier Inc. All rights reserved.