Estimation of Markov Processes with Levy Type Generators

This paper discusses methods for the estimation of a class of Markov processes with Levy type generators. This work supplements a number of existing approaches by allowing for state dependent jumps of possibly infinite intensity. It is shown how moment conditions can be generated along with a simple method for obtaining the optimal weighting matrix. Conditions under which estimatorsthat are asymptotically equivalent to the infeasible maximum likelihood estimator can be constructed are presented.