On Coupling of continuous-time renewal processes
- 1 March 1982
- journal article
- Published by Cambridge University Press (CUP) in Journal of Applied Probability
- Vol. 19 (1) , 82-89
- https://doi.org/10.2307/3213918
Abstract
This paper shows how the coupling method applies to renewal theory in continuous time. Old and new rate results for tendency towards equilibrium and forgetfulness of initial delay are obtained. The coupling approach also provides a new way of analysing the asymptotics of functions of renewal processes which avoids the route via a renewal equation.Keywords
This publication has 7 references indexed in Scilit:
- A refinement of the coupling method in renewal theoryStochastic Processes and their Applications, 1981
- On coupling of discrete renewal processesProbability Theory and Related Fields, 1979
- Uniform limit theorems for non-singular renewal and Markov renewal processesJournal of Applied Probability, 1978
- A splitting technique for Harris recurrent Markov chainsProbability Theory and Related Fields, 1978
- A new approach to the limit theory of recurrent Markov chainsTransactions of the American Mathematical Society, 1978
- Uniform rates of convergence for Markov chain transition probabilitiesProbability Theory and Related Fields, 1974
- On Absolutely Continuous Components and Renewal TheoryThe Annals of Mathematical Statistics, 1966