Spectral Analysis of Markov Kernels and Application to the Convergence Rate Of Discrete Random Walks

Abstract

Let {Xn}n∈ℕbe a Markov chain on a measurable spacewith transition kernelP, and letThe Markov kernelPis here considered as a linear bounded operator on the weighted-supremum spaceassociated withV. Then the combination of quasicompactness arguments with precise analysis of eigenelements ofPallows us to estimate the geometric rate of convergence ρV(P) of {Xn}n∈ℕto its invariant probability measure in operator norm onA general procedure to compute ρV(P) for discrete Markov random walks with identically distributed bounded increments is specified.