1978/03/01 by Anthony G. Pakes
Business, Management and Accounting · Mathematics · #Absorbing Markov chain #Additive Markov chain #Advanced Queuing Theory Analysis #Algorithm #Applied mathematics #Chain (unit) #Combinatorics #Distribution (mathematics) #Limit (mathematics) #Limiting #Markov Chains and Monte Carlo Methods #Markov chain #Markov chain mixing time #Markov model #Markov process #Markov property #Mathematical analysis #Mathematics #Random walk #State (computer science) #Statistical physics #Statistics #Stochastic processes and statistical mechanics
paper · doi:10.2307/3213237
openalex publication_date 1978/03/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/05/21
This paper develops the notion of the limiting age of an absorbing Markov chain, conditional on the present state. Chains with a single absorbing state 0 are considered and with such a chain can be associated a return chain, obtained by restarting the original chain at a fixed state after each absorption. The limiting age, A ( j ), is the weak limit of the time given X n = j (n → ∞). A criterion for the existence of this limit is given and this is shown to be fulfilled in the case of the return chains constructed from the Galton–Watson process and the left-continuous random walk. Limit theorems for A ( J ) ( J → ∞) are given for these examples.