Probability Theory and Related Fields

, Volume 79, Issue 2, pp 271–287

Uniqueness in law for pure jump Markov processes

  • R. F. Bass
Article

DOI: 10.1007/BF00320922

Cite this article as:
Bass, R.F. Probab. Th. Rel. Fields (1988) 79: 271. doi:10.1007/BF00320922

Summary

Let A be the operator defined on C2 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.

Copyright information

© Springer-Verlag 1988

Authors and Affiliations

  • R. F. Bass
    • 1
  1. 1.Department of MathematicsUniversity of WashingtonSeattleUSA

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