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Renewal theorems and mixing for non Markov flows with infinite measure

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Melbourne, Ian and Terhesiu, Dalia (2020) Renewal theorems and mixing for non Markov flows with infinite measure. Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques, 56 (1). pp. 449-476. doi:10.1214/19-AIHP968 ISSN 0246-0203.

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Official URL: https://doi.org/10.1214/19-AIHP968

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Abstract

We obtain results on mixing for a large class of (not necessarily Markov) infinite measure semiflows and flows. Erickson proved, amongst other things, a strong renewal theorem in the corresponding i.i.d. setting. Using operator renewal theory, we extend Erickson’s methods to the deterministic (i.e. non-i.i.d.) continuous time setting and obtain results on mixing as a consequence.

Item Type: Journal Article
Subjects: Q Science > QA Mathematics
T Technology > T Technology (General)
Divisions: Faculty of Science, Engineering and Medicine > Science > Mathematics
Library of Congress Subject Headings (LCSH): Renewal theory, Markov processes, Processes, Infinite
Journal or Publication Title: Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques
Publisher: Institute Henri Poincaré
ISSN: 0246-0203
Official Date: 1 February 2020
Dates:
DateEvent
1 February 2020Published
13 February 2019Accepted
Volume: 56
Number: 1
Page Range: pp. 449-476
DOI: 10.1214/19-AIHP968
Status: Peer Reviewed
Publication Status: Published
Access rights to Published version: Open Access (Creative Commons)
Date of first compliant deposit: 13 February 2019
Date of first compliant Open Access: 19 February 2021
RIOXX Funder/Project Grant:
Project/Grant IDRIOXX Funder NameFunder ID
ESIEuropean Commissionhttp://dx.doi.org/10.13039/501100000780
ERC AdG 320977European Research Councilhttp://dx.doi.org/10.13039/501100000781
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