Generalized Mehler Semigroups: The Non-Gaussian Case |
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Authors: | Fuhrman Marco Röckner Michael |
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Institution: | (1) Dipartimento di Matematica, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133 Milano, Italy;(2) Fakultät für Mathematik, Universität Bielefeld, Postfach 100131, 33501 Bielefeld, Germany |
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Abstract: | We study generalized Mehler semigroups, introduced in 7], with special emphasis on the non-Gaussian case. We review and simplify the method of construction. In the general (non-Gaussian) case we construct an associated cadlag Markov process in an appropriate state space obtained as a solution of a stochastic equation which can be solved by . We also show tightness of the associated (r, p)-capacities. Invariant measures, time regularity and a definition of the generator are also studied. |
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Keywords: | Markovian semigroups Mehler formula cadlag processes in abstract spaces tightness of capacities |
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