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The multitype branching random walk: temporal and spatial limit theorems

Published online by Cambridge University Press:  01 July 2016

B. Gail Ivanoff
B. Gail Ivanoff*
Affiliation:
University of Ottawa
*
∗Postal address: Department of Mathematics, University of Ottawa, Ottawa, Ontario, Canada K1N 6N5.
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Abstract

We consider a multitype branching random walk with independent Poisson random fields of each type of particle initially. The existence of limiting random fields as the generation number, is studied, when the intensity of the initial field is renormalized in such a way that the mean measures converge. Spatial laws of large numbers and central limit theorems are given for the limiting random field, when it is non-trivial.

Keywords

PROBABILITY GENERATING FUNCTIONALLAPLACE TRANSFORMMOMENT MEASURESLAW OF LARGE NUMBERSCENTRAL LIMIT THEOREM
Type
Research Article
Information
Advances in Applied Probability , Volume 21 , Issue 3 , September 1989 , pp. 491 - 512
Copyright
Copyright © Applied Probability Trust 1989 

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