Limit theorems and structural properties of the cat-and-mouse Markov chain and its generalisations

Limit theorems and structural properties of the cat-and-mouse Markov chain and its generalisations Full article

Journal

Advances in Applied Probability
ISSN: 0001-8678 , E-ISSN: 1475-6064

Output data

Year: 2022, Volume: 54, Number: 1, Pages: 141-166 Pages count : 26 DOI: 10.1017/apr.2021.23

Tags

Cat-and-mouse games, multidimensional Markov chain, compound renewal process, regular variation, weak convergence, randomly stopped sums

Authors

Foss Sergey ^1,2 , Prasolov Timofei ³ , Shneer Seva ^1,3

Affiliations

1	Heriot-Watt University
2	Sobolev Institute of Mathematics
3	Novosibirsk State University

We revisit the so-called cat-and-mouse Markov chain, studied earlier by Litvak and Robert (2012). This is a two-dimensional Markov chain on the lattice , where the first component (the cat) is a simple random walk and the second component (the mouse) changes when the components meet. We obtain new results for two generalisations of the model. First, in the two-dimensional case we consider far more general jump distributions for the components and obtain a scaling limit for the second component. When we let the first component be a simple random walk again, we further generalise the jump distribution of the second component. Secondly, we consider chains of three and more dimensions, where we investigate structural properties of the model and find a limiting law for the last component.

Foss S. , Prasolov T. , Shneer S.
Limit theorems and structural properties of the cat-and-mouse Markov chain and its generalisations
Advances in Applied Probability. 2022. V.54. N1. P.141-166. DOI: 10.1017/apr.2021.23 WOS Scopus РИНЦ OpenAlex

Published online:	Feb 28, 2022
Published print:	Apr 4, 2022

Web of science:	WOS:000814625700003
Scopus:	2-s2.0-85125854045
Elibrary:	48189241
OpenAlex:	W4214771594

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