Branching Processes with Negative Offspring Distributions

Ioana Dumitriu^{1}, Joel Spencer^{2}, and Catherine Yan^{3}

dumitriu@math.mit.edu

spencer@cims.nyu.edu

cyan@math.tamu.edu

Annals of Combinatorics 7 (1) p.35-47 March, 2003

Abstract:

A branching process is a mathematical description of the growth of a population
for which the individual produces offsprings according to stochastic laws. Branching
processes can be modeled by one-dimensional random walks with non-negative integral
step-sizes. In this paper we consider the random walk with a similar algebraic setting
but the step-size distribution is allowed to take negative values. We gave the exact
formula for the limit probability under which the random walk continues forever.
Asymptotic results are also presented.

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