## The Annals of Mathematical Statistics

### Multivariate Competition Processes

Donald L. Iglehart

#### Abstract

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.

#### Article information

Source
Ann. Math. Statist., Volume 35, Number 1 (1964), 350-361.

Dates
First available in Project Euclid: 27 April 2007

https://projecteuclid.org/euclid.aoms/1177703758

Digital Object Identifier
doi:10.1214/aoms/1177703758

Mathematical Reviews number (MathSciNet)
MR164384

Zentralblatt MATH identifier
0143.19902

JSTOR