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Absolute continuity of the invariant measure in piecewise deterministic Markov Processes having degenerate jumps

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  • Löcherbach, E.

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.

Suggested Citation

  • Löcherbach, E., 2018. "Absolute continuity of the invariant measure in piecewise deterministic Markov Processes having degenerate jumps," Stochastic Processes and their Applications, Elsevier, vol. 128(6), pages 1797-1829.
    • Handle: RePEc:eee:spapps:v:128:y:2018:i:6:p:1797-1829
    DOI: 10.1016/j.spa.2017.08.011
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    References listed on IDEAS

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    1. Fournier, Nicolas, 2002. "Jumping SDEs: absolute continuity using monotonicity," Stochastic Processes and their Applications, Elsevier, vol. 98(2), pages 317-330, April.
    2. Bally, Vlad & Caramellino, Lucia, 2011. "Riesz transform and integration by parts formulas for random variables," Stochastic Processes and their Applications, Elsevier, vol. 121(6), pages 1332-1355, June.
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