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

Bass, R. F.; Cranston, M.

Ann. Probab. 14, 490-532 (1986).

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

Keywords:

Malliavin calculus; jointly continuous local times; discontinuous martingales