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Strong Feller properties for degenerate SDEs with jumps. (English. French summary) Zbl 1346.60080

The aim of this paper is twofold. First, applying Malliavin’s calculus, the authors extend the famous Bogachev result concerning the existence and smoothness of the density of the family of multi-dimensional Wiener functionals. Second, this result is applied to establish the strong Feller property of the semigroup determined by a stochastic differential equation driven by subordinate Brownian motions, under full Hörmander conditions.

MSC:

60H07 Stochastic calculus of variations and the Malliavin calculus
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
60G51 Processes with independent increments; Lévy processes
60G52 Stable stochastic processes
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