Advances in Applied Probability

Spectral analysis of Markov kernels and application to the convergence rate of discrete random walks

Loïc Hervé and James Ledoux

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Let {Xn}nN be a Markov chain on a measurable space X with transition kernel P, and let V : X → [1, +∞). The Markov kernel P is here considered as a linear bounded operator on the weighted-supremum space BV associated with V. Then the combination of quasicompactness arguments with precise analysis of eigenelements of P allows us to estimate the geometric rate of convergence ρV(P) of {Xn}nN to its invariant probability measure in operator norm on BV. A general procedure to compute ρV(P) for discrete Markov random walks with identically distributed bounded increments is specified.

Article information

Adv. in Appl. Probab., Volume 46, Number 4 (2014), 1036-1058.

First available in Project Euclid: 12 December 2014

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Zentralblatt MATH identifier

Primary: 60J10: Markov chains (discrete-time Markov processes on discrete state spaces) 47B07: Operators defined by compactness properties

V-geometric ergodicity quasicompactness drift condition birth-and-death Markov chain


Hervé, Loïc; Ledoux, James. Spectral analysis of Markov kernels and application to the convergence rate of discrete random walks. Adv. in Appl. Probab. 46 (2014), no. 4, 1036--1058. doi:10.1239/aap/1418396242.

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