Absolute continuity of the invariant measure in piecewise deterministic Markov Processes having degenerate jumps |
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Authors: | E Löcherbach |
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Institution: | CNRS UMR 8088, Département de Mathématiques, Université de Cergy-Pontoise, 2 avenue Adolphe Chauvin, 95302 Cergy-Pontoise Cedex, France |
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Abstract: | We consider piecewise deterministic Markov processes with degenerate transition kernels of the house-of-cards- type. We use a splitting scheme based on jump times to prove the absolute continuity, as well as some regularity, of the invariant measure of the process. Finally, we obtain finer results on the regularity of the one-dimensional marginals of the invariant measure, using integration by parts with respect to the jump times. |
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Keywords: | primary 60Hxx secondary 60J75 60G55 Piecewise deterministic Markov processes Invariant measure Integration by parts based on jump times Jump processes |
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