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March, 1964 Multivariate Competition Processes
Donald L. Iglehart
Ann. Math. Statist. 35(1): 350-361 (March, 1964). DOI: 10.1214/aoms/1177703758


A multivariate competition process (M.C.P.) is a stationary, continuous time Markov process whose state space is the lattice points of the positive orthant in $N$-dimensional space and whose transition probability matrix only allows jumps to certain nearest neighbors. As such it is the natural generalization of birth and death processes. In this paper we extend the results of Reuter [15] to obtain sufficient conditions for a M.C.P. to be regular, positive recurrent, absorbed with certainty, and to have finite mean absorption time. Some explicit examples are given and references to various applications indicated.


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Donald L. Iglehart. "Multivariate Competition Processes." Ann. Math. Statist. 35 (1) 350 - 361, March, 1964.


Published: March, 1964
First available in Project Euclid: 27 April 2007

zbMATH: 0143.19902
MathSciNet: MR164384
Digital Object Identifier: 10.1214/aoms/1177703758

Rights: Copyright © 1964 Institute of Mathematical Statistics

Vol.35 • No. 1 • March, 1964
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