## The Annals of Mathematical Statistics

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

### Multivariate Competition Processes

#### 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

**Permanent link to this document**

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**

links.jstor.org

#### Citation

Iglehart, Donald L. Multivariate Competition Processes. Ann. Math. Statist. 35 (1964), no. 1, 350--361. doi:10.1214/aoms/1177703758. https://projecteuclid.org/euclid.aoms/1177703758