Large deviations for empirical measures of self-interacting Markov chains

Amarjit Budhiraja, Adam Waterbury and Pavlos Zoubouloglou

Stochastic Processes and their Applications, 2025, vol. 186, issue C

Abstract: Let Δo be a finite set and, for each probability measure m on Δo, let G(m) be a transition kernel on Δo. Consider the sequence {Xn} of Δo-valued random variables such that, given X0,…,Xn, the conditional distribution of Xn+1 is G(Ln+1)(Xn,⋅), where Ln+1=1n+1∑i=0nδXi. Under conditions on G we establish a large deviation principle for the sequence {Ln}. As one application of this result we obtain large deviation asymptotics for the Aldous et al. (1988) approximation scheme for quasi-stationary distributions of finite state Markov chains. The conditions on G cover other models as well, including certain models with edge or vertex reinforcement.

Keywords: Reinforced random walks; Quasi-stationary distributions; Empirical measure; Large deviations; Stochastic approximations; Self-interacting Markov chains; Multiscale systems (search for similar items in EconPapers)
Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S030441492500081X
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:186:y:2025:i:c:s030441492500081x

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.2025.104640

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 ().