An estimate of the stability for nonhomogeneous Markov chains under classical minorization condition

2014 ◽  
Vol 88 ◽  
pp. 35-49 ◽  
Author(s):  
V. V. Golomozyĭ
Keyword(s):  
Markov Chains ◽  
Nonhomogeneous Markov Chains ◽  
Minorization Condition ◽  
The Stability

Stability of functionals of perturbed Markov chains under the condition of uniform minorization

2020 ◽  
Vol 28 (4) ◽  
pp. 237-251
Author(s):  
Vitaliy Golomoziy
Keyword(s):  
Markov Chains ◽  
Large Deviations ◽  
State Space ◽  
Discrete Time ◽  
Stability Estimates ◽  
General State ◽  
Whole Space ◽  
Minorization Condition ◽  
General State Space ◽  
The Stability

AbstractIn this paper, we investigate the stability of functionals and trajectories of two different, independent, time-inhomogeneous, discrete-time Markov chains on a general state space. We obtain various stability estimates such as an estimate for a difference in expectations of functionals, {L_{2}} stability, and a probability of large deviations. The key condition that is used is the minorization condition on the whole space. We consider different limitations on the functional and on the proximity of two chains. We use the coupling method as a primary technique in our proofs.

SOME LIMIT THEOREMS OF DELAYED AVERAGES FOR COUNTABLE NONHOMOGENEOUS MARKOV CHAINS

2019 ◽  
pp. 1-19
Author(s):  
Pingping Zhong ◽  
Weiguo Yang ◽  
Zhiyan Shi ◽  
Yan Zhang
Keyword(s):  
Information Theory ◽  
Markov Chains ◽  
Limit Theorems ◽  
Law Of Large Numbers ◽  
Strong Law ◽  
Strong Ergodicity ◽  
Large Numbers ◽  
Nonhomogeneous Markov Chains ◽  
Definition Of ◽  
Bivariate Functions

AbstractThe purpose of this paper is to establish some limit theorems of delayed averages for countable nonhomogeneous Markov chains. The definition of the generalized C-strong ergodicity and the generalized uniformly C-strong ergodicity for countable nonhomogeneous Markov chains is introduced first. Then a theorem about the generalized C-strong ergodicity and the generalized uniformly C-strong ergodicity for the nonhomogeneous Markov chains is established, and its applications to the information theory are given. Finally, the strong law of large numbers of delayed averages of bivariate functions for countable nonhomogeneous Markov chains is proved.

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