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

Richard F. Bass

Stochastic Processes and their Applications, 1988, vol. 29, issue 1, 65-83

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.

Keywords: pure; jump; Markov; processes; stable-like; processes; local; times; occupation; times; symmetric; stable; processes; purely; discontinuous; martingales; pseudodifferential; operators (search for similar items in EconPapers)
Date: 1988
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