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On a general random exchange model

Published online by Cambridge University Press:  14 July 2016

Inge S. Helland  and
Trygve S. Nilsen
Inge S. Helland
Affiliation:
University of Bergen
Trygve S. Nilsen
Affiliation:
University of Bergen
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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

EXCHANGE MODELEXTREME VALUE THEORYLIMITING DISTRIBUTION

Information

Type
Research Papers
Information
Journal of Applied Probability , Volume 13 , Issue 4 , December 1976 , pp. 781 - 790
Copyright
Copyright © Applied Probability Trust 1976 

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