Martingale Nature and Laws of the Iterated Logarithm for Markov Processes of Pure-Jump Type

Abstract

We present sufficient conditions, in terms of the jumping kernels, for two large classes of conservative Markov processes of pure-jump type to be purely discontinuous martingales with finite second moment. As an application, we establish the law of the iterated logarithm for sample paths of the associated processes.

Final version, to appear in Journal of Theoretical Probability