## The Annals of Probability

### Limiting Distributions and Regeneration Times for Multitype Branching Processes with Immigration in a Random Environment

Eric S. Key

#### Abstract

Sufficient conditions for the existence of a limiting distribution for a multitype branching process with immigration in a random environment, $Z(t)$, are given. In the case when the environment is an independent, identically distributed sequence, sufficient conditions are given which insure that the tail of the distribution of $\nu = \inf\{t > 0: Z(t) = 0\}$ decreases exponentially fast, and an application of this fact to random walk in a random environment is indicated.

#### Article information

Source
Ann. Probab., Volume 15, Number 1 (1987), 344-353.

Dates
First available in Project Euclid: 19 April 2007

https://projecteuclid.org/euclid.aop/1176992273

Digital Object Identifier
doi:10.1214/aop/1176992273

Mathematical Reviews number (MathSciNet)
MR877607

Zentralblatt MATH identifier
0623.60090

JSTOR