Selecting the last success in Markov-dependent trials

2002 ◽  
Vol 39 (02) ◽  
pp. 271-281 ◽  
Author(s):  
Shoou-Ren Hsiau ◽  
Jiing-Ru Yang
Keyword(s):  
Markov Chains ◽  
Optimal Strategy ◽  
Homogeneous Case ◽  
Nonhomogeneous Markov Chains ◽  
Markov Dependent Trials ◽  
Independence Structure

In a sequence of Markov-dependent trials, the optimal strategy which maximizes the probability of stopping on the last success is considered. Both homogeneous Markov chains and nonhomogeneous Markov chains are studied. For the homogeneous case, the analysis is divided into two parts and both parts are realized completely. For the nonhomogeneous case, we prove a result which contains the result of Bruss (2000) under an independence structure.

Selecting the last success in Markov-dependent trials

2002 ◽  
Vol 39 (2) ◽  
pp. 271-281 ◽  
Author(s):  
Shoou-Ren Hsiau ◽  
Jiing-Ru Yang
Keyword(s):  
Markov Chains ◽  
Optimal Strategy ◽  
Homogeneous Case ◽  
Nonhomogeneous Markov Chains ◽  
Markov Dependent Trials ◽  
Independence Structure

In a sequence of Markov-dependent trials, the optimal strategy which maximizes the probability of stopping on the last success is considered. Both homogeneous Markov chains and nonhomogeneous Markov chains are studied. For the homogeneous case, the analysis is divided into two parts and both parts are realized completely. For the nonhomogeneous case, we prove a result which contains the result of Bruss (2000) under an independence structure.

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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