, Volume 79, Issue 2, pp 271-287

Uniqueness in law for pure jump Markov processes

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Summary

Let A be the operator defined on C 2 functions by $$Af\left( x \right) = \smallint \left[ {f\left( {x + h} \right) - f\left( x \right) - f'\left( x \right)h 1_{([ - 1, 1])} \left( h \right)} \right]v\left( {x,dh} \right).$$ 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.

Partially supported by NSF grant DMS 85-00581