Spectral theoretic characterisation of Markov chain convergence

Autor:	Davies, Bryn, Xiao, Yu
Rok vydání:	2024
Předmět:	Mathematics - Dynamical Systems Mathematics - Classical Analysis and ODEs Mathematics - Probability 37A05 34L05 58J51
Druh dokumentu:	Working Paper
Popis:	In this work, we characterise the statistics of Markov chains by constructing an associated sequence of periodic differential operators. Studying the density of states of these operators reveals the absolutely continuous invariant measure of the Markov chain. This approach also leads to a direct proof of convergence to the invariant measure, along with explicit convergence rates. We show how our method can be applied to a class of related Markov chains including the logistic map, the tent map and Chebyshev maps of arbitrary order. Comment: 24 pages, 8 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2410.15829 Zobrazit plný text záznamu View this record from Arxiv