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

Giovanni Conforti; Christian Léonard

doi:10.1016/j.spa.2021.10.002

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

Giovanni Conforti
, Christian Léonard

Université Paris-Nanterre

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	85-124
Number of pages	40
Journal	Stochastic Processes and their Applications
Volume	144
DOIs	https://doi.org/10.1016/j.spa.2021.10.002
Publication status	Published - 1 Feb 2022

Keywords

Jump process
Relative entropy
Time reversal

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10.1016/j.spa.2021.10.002

Cite this

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title = "Time reversal of Markov processes with jumps under a finite entropy condition",

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 carr{\'e} du champ of a Markov process recently obtained in Cattiaux et al. (2021), and using an entropic improvement strategy discovered by F{\"o}llmer (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.",

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AU - Léonard, Christian

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N2 - 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.

AB - 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.

KW - Jump process

KW - Relative entropy

KW - Time reversal

U2 - 10.1016/j.spa.2021.10.002

DO - 10.1016/j.spa.2021.10.002

M3 - Article

AN - SCOPUS:85119421792

SN - 0304-4149

VL - 144

SP - 85

EP - 124

JO - Stochastic Processes and their Applications

JF - Stochastic Processes and their Applications

ER -

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

Abstract

Keywords

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