On a general random exchange model
- 1 December 1976
- journal article
- Published by Cambridge University Press (CUP) in Journal of Applied Probability
- Vol. 13 (4) , 781-790
- https://doi.org/10.2307/3212533
Abstract
Two independent i.i.d. sequences of random variables {Un} and {Dn} generate a Markov process {Xn} by Xn = max(Xn–1 – Dn, Un), n = 1, 2, …. ‘Exchange’ is defined as the event [Un > Xn–1 – Dn]. Conditions for existence of a limiting distribution for {Xn} are established, and normalization is discussed when no limiting distribution exists. Finally the process {Xn at the k th exchange; k = l, 2, …} and the time between consecutive exchanges are considered.Keywords
This publication has 5 references indexed in Scilit:
- Deep Water Exchanges in a Sill Fjord: A Stochastic ProcessJournal of Physical Oceanography, 1973
- Extremal processes and record value timesJournal of Applied Probability, 1973
- The theory of queues with a single serverMathematical Proceedings of the Cambridge Philosophical Society, 1952
- On certain limit theorems of the theory of probabilityBulletin of the American Mathematical Society, 1946
- Sur La Distribution Limite Du Terme Maximum D'Une Serie AleatoireAnnals of Mathematics, 1943