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Integration by parts for jump processes. (English) Zbl 0649.60080
Séminaire de probabilités XXII, Strasbourg/France, Lect. Notes Math. 1321, 271-315 (1988).
[For the entire collection see Zbl 0635.00013.]
Estimates and smoothness properties of the transition and resolvent densities of position-dependent Markov jump processes are obtained by means of an integration by parts formula, sometimes called Malliavin calculus for jump processes. In the position-independent case such results are easily available using the Fourier transform: a comparison shows that the results for the general case are nearly as good as one could hope for.
Reviewer: J.R.Norris

60J35 Transition functions, generators and resolvents
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
60G30 Continuity and singularity of induced measures
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