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Branching Processes with Negative Offspring Distributions
Ioana Dumitriu1, Joel Spencer2, and Catherine Yan3
1Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
2Courant Institute of Mathematical Sciences, New York University, New York, NY 10012, USA
3Department of Mathematics, Texas A & M University, College Station, TX 77843, USA
Annals of Combinatorics 7 (1) p.35-47 March, 2003
AMS Subject Classification: 05A16, 05D40, 60J80
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.
Keywords: branching processes, negative offsprings


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