Spaces of Summable Sequences in Renewal Theory and the Theory of Markov Chains

1981 ◽  
Vol 104 (1) ◽  
pp. 119-128 ◽  
Author(s):  
Laurie Davies ◽  
Rudolf Grübel
Keyword(s):  
Markov Chains ◽  
Renewal Theory

scholarly journals Theory of semiregenerative phenomena

1988 ◽  
Vol 25 (A) ◽  
pp. 257-274
Author(s):  
N. U. Prabhu
Keyword(s):  
Markov Chains ◽  
Discrete Time ◽  
Renewal Process ◽  
Renewal Theory ◽  
Markov Renewal Process ◽  
Discrete Time Case ◽  
Markov Renewal Theory

We develop a theory of semiregenerative phenomena. These may be viewed as a family of linked regenerative phenomena, for which Kingman [6], [7] developed a theory within the framework of quasi-Markov chains. We use a different approach and explore the correspondence between semiregenerative sets and the range of a Markov subordinator with a unit drift (or a Markov renewal process in the discrete-time case). We use techniques based on results from Markov renewal theory.

scholarly journals Renewal theory for transient Markov chains with asymptotically zero drift

2020 ◽  
Vol 373 (10) ◽  
pp. 7253-7286
Author(s):  
Denis Denisov ◽  
Dmitry Korshunov ◽  
Vitali Wachtel
Keyword(s):  
Markov Chains ◽  
Renewal Theory ◽  
Zero Drift

scholarly journals Theory of semiregenerative phenomena

1988 ◽  
Vol 25 (A) ◽  
pp. 257-274 ◽  
Author(s):  
N. U. Prabhu
Keyword(s):  
Markov Chains ◽  
Discrete Time ◽  
Renewal Process ◽  
Renewal Theory ◽  
Markov Renewal Process ◽  
Discrete Time Case ◽  
Markov Renewal Theory

We develop a theory of semiregenerative phenomena. These may be viewed as a family of linked regenerative phenomena, for which Kingman [6], [7] developed a theory within the framework of quasi-Markov chains. We use a different approach and explore the correspondence between semiregenerative sets and the range of a Markov subordinator with a unit drift (or a Markov renewal process in the discrete-time case). We use techniques based on results from Markov renewal theory.

Renewal-type behavior of absorption times in Markov chains

1994 ◽  
Vol 26 (4) ◽  
pp. 988-1005 ◽  
Author(s):  
Bernard Van Cutsem ◽  
Bernard Ycart
Keyword(s):  
Asymptotic Behavior ◽  
Markov Chain ◽  
Limit Theorem ◽  
Markov Chains ◽  
Transition Matrix ◽  
Renewal Theory ◽  
Stochastic Comparison ◽  
Absorption Time ◽  
Starting Point ◽  
Lower Triangular

This paper studies the absorption time of an integer-valued Markov chain with a lower-triangular transition matrix. The main results concern the asymptotic behavior of the absorption time when the starting point tends to infinity (asymptotics of moments and central limit theorem). They are obtained using stochastic comparison for Markov chains and the classical theorems of renewal theory. Applications to the description of large random chains of partitions and large random ordered partitions are given.

scholarly journals Renewal Theory for Markov Chains on the Real Line

1982 ◽  
Vol 10 (4) ◽  
pp. 942-954 ◽  
Author(s):  
Robert W. Keener
Keyword(s):  
Markov Chains ◽  
Real Line ◽  
Renewal Theory ◽  
The Real
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