Uniqueness in law for pure jump Markov processes

Abstract

Let A be the operator defined on C2 functions by {Mathematical expression} Sufficient conditions are given for existence and uniqueness for the martingale problem associated with A. In the case of stable-like processes, where v(x, dh) is equal to the Lévy measure for the stable symmetric process of index α(x) for each x, the conditions reduce to α(x) continuous for existence and α(x) Dini continuous for uniqueness. © 1988 Springer-Verlag.