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On parabolic inequalities for generators of diffusions with jumps |
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| Authors: | Vladimir I. Bogachev Michael Röckner Stanislav V. Shaposhnikov |
| Affiliation: | 1. Department of Mechanics and Mathematics, Moscow State University, 119991, Moscow, Russia 2. Department of Informatics and Applied Mathematics, St. Tikhon’s Orthodox University, Moscow, Russia 3. Fakult?t für Mathematik, Universit?t Bielefeld, 33501, Bielefeld, Germany |
| Abstract: | We prove absolute continuity of space-time probabilities satisfying certain parabolic inequalities for generators of diffusions with jumps. As an application, we prove absolute continuity of transition probabilities of singular diffusions with jumps under minimal conditions that ensure absolute continuity of the corresponding diffusions without jumps. |
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