Abstract
Let {Xn}n∈N 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}n∈N 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.
Citation
Loïc Hervé. James Ledoux. "Spectral analysis of Markov kernels and application to the convergence rate of discrete random walks." Adv. in Appl. Probab. 46 (4) 1036 - 1058, December 2014. https://doi.org/10.1239/aap/1418396242
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