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).
pp. 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 |
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Depositing User: | Symplectic Admin |
Date Deposited: | 08 Apr 2020 10:32 |
Last Modified: | 18 Jan 2023 23:56 |
DOI: | 10.1017/s0963548320000024 |
Related URLs: | |
URI: | https://livrepository.liverpool.ac.uk/id/eprint/3081723 |