We investigate the convergence of nonhomogeneous Markov chains in general state space by using the f norm and the coupling method, and thus, a sufficient condition for the convergence of nonhomogeneous Markov chains in general state space is obtained.
Zhifeng ZHU
,
Shaoyi ZHANG
,
Fanji TIAN
. THE CONVERGENCE OF NONHOMOGENEOUS MARKOV CHAINS IN GENERAL STATE SPACES BY THE COUPLING METHOD[J]. Acta mathematica scientia, Series B, 2021
, 41(5)
: 1777
-1787
.
DOI: 10.1007/s10473-021-0523-4
[1] Meyn S P, Tweedie R L. Markov Chains and Stochastic Stability. London:Springer Verlag, 2008
[2] Kartashov N V. Inequalities in theorems of ergodicity and stability for Markov chains with common phase space, I. Probab Theor Appl, 1986, 30:247-259
[3] Mukhamedov F. Weak ergodicity of nonhomogeneous Markov chains on noncom-mutative L1-spaces. Banach J Math Anal, 2013, 7:53-73
[4] Mukhamedov F. Ergodic properties of nonhomogeneous Markov chains dened on ordered Banach spaces with a base. Acta Math Hungar, 2015, 147:294-323
[5] Chen M F. From Markov Chains to Non-equilibrium Particle Systems. 2nd ed. Singapore:World Scientific, 2004
[6] Gong G L, Qian M P. A Course in Appied Stochastic Processes and Stochastic Models in Algorithms and Intelligence Computation. Beijing:Tsinghua University Press, 2004
[7] Zhang S Y. The Existence and Application of Optimal Markow Coupling[D]. Beijing Normal University, 2000
[8] Zhu Z F, Zhang S Y. Study on the convergence of nonhomogeneous Markov chains with probability distance. Acta Mathematica Scientia, 2018, 38A(5):963-969
[9] Lindvall T. Lectures on the Coupling Method. New York:Wiley, 1992
[10] Zhu Z F, Zhang S Y. Study of f-exponent ergodic of Markov chains by coupling method. Acta Mathematica Sinica, 2019, (3):287-292