Pseudo differential operators with negative definite symbols and the martingale problem

Abstract

Pseudo differential operators with negative definite symbols p(x,ξ) arise as generators of Markov processes in a natural way. In this article we solve the martingale problem for this class of operators supposing only some boundedness condition for the symbol and prove uniqueness of the solution under the assumption that the symbol is sufficiently smooth with respect to x and comparable with a fixed negative definite function in a suitable way