Deviation inequalities for contractive infinite memory processes

Paul Doukhan and Xiequan Fan

Stochastic Processes and their Applications, 2026, vol. 191, issue C

Abstract: In this paper, we introduce a class of stochastic processes that encompasses many natural and widely used examples. A key feature of these processes is their infinite memory, which enables them to retain information from arbitrarily distant past states. Using the martingale decomposition method, we derive deviation and moment inequalities for separately Lipschitz functionals of such processes, under various moment conditions on certain dominating random variables. Our results extend those obtained for Markov chains by Dedecker and Fan [Stochastic Process. Appl., 2015], as well as recent results by Chazottes et al. [Ann. Appl. Probab., 2023] concerning specific infinite-memory models with sub-Gaussian concentration bounds. We also discuss an application to the stochastic gradient Langevin dynamics algorithm.

Keywords: Martingales; Deviation inequalities; Infinite memory; Moment inequalities (search for similar items in EconPapers)
Date: 2026
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0304414925002224
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:191:y:2026:i:c:s0304414925002224

Ordering information: This journal article can be ordered from
http://http://www.elsevier.com/wps/find/supportfaq.cws_home/regional
https://shop.elsevie ... _01_ooc_1&version=01

DOI: 10.1016/j.spa.2025.104778

Access Statistics for this article

Stochastic Processes and their Applications is currently edited by T. Mikosch

More articles in Stochastic Processes and their Applications from Elsevier
Bibliographic data for series maintained by Catherine Liu ().