On the Relation between Limit Theorems of Finite Groups and an Ergodic Theorem for Markov Chains with Doubly Stochastic Transition Matrices

1965 ◽  
Vol 10 (3) ◽  
pp. 493-496 ◽  
Author(s):  
V. M. Maksimov
Keyword(s):  
Markov Chains ◽  
Ergodic Theorem ◽  
Finite Groups ◽  
Limit Theorems ◽  
Transition Matrices ◽  
Doubly Stochastic ◽  
Stochastic Transition

Cheeger inequalities for absorbing Markov chains

2016 ◽  
Vol 48 (3) ◽  
pp. 631-647
Author(s):  
Gary Froyland ◽  
Robyn M. Stuart
Keyword(s):  
Markov Chains ◽  
Transition Probability ◽  
Transition Probability Matrix ◽  
Transition Matrices ◽  
Stochastic Transition ◽  
Absorbing Markov Chains ◽  
Second Eigenvalue

Abstract We construct Cheeger-type bounds for the second eigenvalue of a substochastic transition probability matrix in terms of the Markov chain's conductance and metastability (and vice versa) with respect to its quasistationary distribution, extending classical results for stochastic transition matrices.

Trace inequalities for mixtures of Markov chains

1977 ◽  
Vol 9 (04) ◽  
pp. 747-764
Author(s):  
Burton Singer ◽  
Seymour Spilerman
Keyword(s):  
Markov Chains ◽  
Special Kind ◽  
Probability Measures ◽  
Stochastic Matrices ◽  
Transition Matrices ◽  
Time Intervals ◽  
Panel Studies ◽  
Image Position ◽  
Trace Inequalities

In a wide variety of multi-wave panel studies in economics and sociology, comparisons between the observed transition matrices and predictions of them based on time-homogeneous Markov chains have revealed a special kind of discrepancy: the trace of the observed matrices tends to be larger than the trace of the predicted matrices. A common explanation for this discrepancy has been via mixtures of Markov chains. Specializing to mixtures of Markov semi-groups of the form we exhibit classes of stochastic matrices M, probability measures µ and time intervals Δ such that for k = 2, 3 and 4. These examples contradict the substantial literature which suggests — implicitly — that the above inequality should be reversed for general mixtures of Markov semi-groups.

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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