On a general random exchange model
- 1 March 1976
- journal article
- research article
- Published by Cambridge University Press (CUP) in Journal of Applied Probability
- Vol. 13 (04) , 781-790
- https://doi.org/10.1017/s0021900200104449
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
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