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The Malliavin calculus for pure jump processes and applications to local time. (English) Zbl 0595.60044

The basis of Malliavin calculus is introduced for various processes including jump processes. Bismut approach is exploited. The existence of \(L^ p\)- and \(C^{\alpha}\)-densities for pure jump Markov processes is established. The existence of jointly continuous local times for purely discontinuous martingales is obtained.
Reviewer: A.Yu.Veretennikov

MSC:

60G30 Continuity and singularity of induced measures
60G44 Martingales with continuous parameter
60J35 Transition functions, generators and resolvents
60J55 Local time and additive functionals
60G57 Random measures
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