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Time reversal of Markov processes with jumps under a finite entropy condition

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  • Conforti, Giovanni
  • Léonard, Christian

Abstract

Motivated by entropic optimal transport, time reversal of Markov jump processes in Rn is investigated. Relying on an abstract integration by parts formula for the carré du champ of a Markov process recently obtained in Cattiaux et al. (2021), and using an entropic improvement strategy discovered by Föllmer (1985, 1986), we compute the semimartingale characteristics of the time reversed process for a wide class of jump processes in Rn with possibly unbounded variation sample paths and singular intensities of jump.

Suggested Citation

  • Conforti, Giovanni & Léonard, Christian, 2022. "Time reversal of Markov processes with jumps under a finite entropy condition," Stochastic Processes and their Applications, Elsevier, vol. 144(C), pages 85-124.
    • Handle: RePEc:eee:spapps:v:144:y:2022:i:c:p:85-124
    DOI: 10.1016/j.spa.2021.10.002
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    References listed on IDEAS

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    1. Gentil, Ivan & Léonard, Christian & Ripani, Luigia & Tamanini, Luca, 2020. "An entropic interpolation proof of the HWI inequality," Stochastic Processes and their Applications, Elsevier, vol. 130(2), pages 907-923.
    2. Yongxin Chen & Tryphon T. Georgiou & Michele Pavon, 2016. "On the Relation Between Optimal Transport and Schrödinger Bridges: A Stochastic Control Viewpoint," Journal of Optimization Theory and Applications, Springer, vol. 169(2), pages 671-691, May.
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