On a general random exchange model

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.