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Malliavin calculus for stable processes on Heisenberg group. (English) Zbl 0785.60028

Malliavin’s calculus for symmetric stable semigroups and truncated stable semigroups of measures on the Heisenberg group is investigated. In particular, \(C^ \infty\)-smoothness is obtained for truncated stable semigroups of the class \(C^ 1\) with a compact support, and, more generally, for densities of the same class \(C^ 1\) which rapidly decrease at infinity.

MSC:

60H07 Stochastic calculus of variations and the Malliavin calculus
60B15 Probability measures on groups or semigroups, Fourier transforms, factorization
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