Analysis of non-reversible Markov chains via similarity orbits



Choi, Michael CH and Patie, Pierre ORCID: 0000-0003-4221-0439
(2020) Analysis of non-reversible Markov chains via similarity orbits. Combinatorics, Probability and Computing, 29 (4). 508 - 536.

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Abstract

<jats:title>Abstract</jats:title><jats:p>In this paper we develop an in-depth analysis of non-reversible Markov chains on denumerable state space from a similarity orbit perspective. In particular, we study the class of Markov chains whose transition kernel is in the similarity orbit of a normal transition kernel, such as that of birth–death chains or reversible Markov chains. We start by identifying a set of sufficient conditions for a Markov chain to belong to the similarity orbit of a birth–death chain. As by-products, we obtain a spectral representation in terms of non-self-adjoint resolutions of identity in the sense of Dunford [21] and offer a detailed analysis on the convergence rate, separation cutoff and L<jats:sup>2</jats:sup>-cutoff of this class of non-reversible Markov chains. We also look into the problem of estimating the integral functionals from discrete observations for this class. In the last part of this paper we investigate a particular similarity orbit of reversible Markov kernels, which we call the pure birth orbit, and analyse various possibly non-reversible variants of classical birth–death processes in this orbit.</jats:p>

Item Type: Article
Depositing User: Symplectic Admin
Date Deposited: 08 Apr 2020 10:32
Last Modified: 06 Jan 2022 08:29
DOI: 10.1017/s0963548320000024
URI: https://livrepository.liverpool.ac.uk/id/eprint/3081723