scholarly journals Renewal theory and computable convergence rates for geometrically ergodic Markov chains

2005 ◽  
Vol 15 (1B) ◽  
pp. 700-738 ◽  
Author(s):  
Peter H. Baxendale
Keyword(s):  
Markov Chains ◽  
Convergence Rates ◽  
Renewal Theory

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.

On records and related processes for sequences with trends

1999 ◽  
Vol 36 (3) ◽  
pp. 668-681 ◽  
Author(s):  
K. Borovkov
Keyword(s):  
Markov Chains ◽  
Limit Theorems ◽  
Convergence Rates ◽  
Rate Function ◽  
Regular Case ◽  
Limiting Distributions ◽  
Record Times ◽  
Ergodicity Theorem ◽  
Linear Trends

We study the records and related variables for sequences with linear trends. We discuss the properties of the asymptotic rate function and relationships between the distribution of the long-term maxima in the sequence and that of a particular observation, including two characterization type results. We also consider certain Markov chains related to the process of records and prove limit theorems for them, including the ergodicity theorem in the regular case (convergence rates are given under additional assumptions), and derive the limiting distributions for the inter-record times and increments of records.

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
Sign in / Sign up

Export Citation Format

Share Document