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Occupation time densities for stable-like processes and other pure jump Markov processes

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  • Bass, Richard F.

Abstract

Pure jump Markov processes Xt on the line associated to the operators A[latin small letter f with hook](x)= [integral operator][[latin small letter f with hook](x+h)-[latin small letter f with hook](x)-[latin small letter f with hook]'(x)hl([-1,1])(h)][nu](x,dh) are considered. Sufficient conditions for Xt to have local times that serve as occupation time densities are given. In the case where [nu](x,dh)= h-(1+[alpha](x)), the stable-like case, these conditions reduce to: inf [alpha](x)>1 and [alpha](x) Dini continuous.

Suggested Citation

  • Bass, Richard F., 1988. "Occupation time densities for stable-like processes and other pure jump Markov processes," Stochastic Processes and their Applications, Elsevier, vol. 29(1), pages 65-83.
    • Handle: RePEc:eee:spapps:v:29:y:1988:i:1:p:65-83
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    Cited by:

    1. Bass, Richard F. & Tang, Huili, 2009. "The martingale problem for a class of stable-like processes," Stochastic Processes and their Applications, Elsevier, vol. 119(4), pages 1144-1167, April.

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