Yet Another Look at Harris’ Ergodic Theorem for Markov Chains

The aim of this note is to present an elementary proof of a variation of Harris’ ergodic theorem of Markov chains.

[1]  T. E. Harris The Existence of Stationary Measures for Certain Markov Processes , 1956 .

[2]  R. Khasminskii Stochastic Stability of Differential Equations , 1980 .

[3]  E. Nummelin General irreducible Markov chains and non-negative operators: List of symbols and notation , 1984 .

[4]  P. Ney GENERAL IRREDUCIBLE MARKOV CHAINS AND NON‐NEGATIVE OPERATORS (Cambridge Tracts in Mathematics, 83) , 1986 .

[5]  K. S. Chan A note on the geometric ergodicity of a Markov chain , 1989, Advances in Applied Probability.

[6]  S. Meyn,et al.  Stability of Markovian processes I: criteria for discrete-time Chains , 1992, Advances in Applied Probability.

[7]  Richard L. Tweedie,et al.  Markov Chains and Stochastic Stability , 1993, Communications and Control Engineering Series.

[8]  S. Meyn,et al.  Computable Bounds for Geometric Convergence Rates of Markov Chains , 1994 .

[9]  J. Rosenthal QUANTITATIVE CONVERGENCE RATES OF MARKOV CHAINS: A SIMPLE ACCOUNT , 2002 .

[10]  M. Ledoux,et al.  On contraction properties of Markov kernels , 2003 .

[11]  R. Douc,et al.  Quantitative bounds on convergence of time-inhomogeneous Markov chains , 2004, math/0503532.

[12]  S. Meyn,et al.  Large Deviations Asymptotics and the Spectral Theory of Multiplicatively Regular Markov Processes , 2005, math/0509310.

[13]  P. Baxendale Renewal theory and computable convergence rates for geometrically ergodic Markov chains , 2005, math/0503515.

[14]  Spectral gaps in Wasserstein distances and the 2D stochastic Navier–Stokes equations , 2006, math/0602479.