Precise estimates of presence probabilities in the branching random walk

Alain Rouault

Stochastic Processes and their Applications, 1993, vol. 44, issue 1, 27-39

Abstract: In the subcritical speed area of a supercritical branching random walk, we prove that when the number of generations grows the probability of presence is asymptotically proportional to the corresponding expectation as in a subcritical Galton-Watson process. This improves a known result on the logarithm of this probability. The basic tools are a discrete version of the Feynman-Kac representation and large deviations.

Keywords: branching; random; walk; non-extinction; probability; large; deviations; Feynman-Kac; representation; local; limit; theorem (search for similar items in EconPapers)
Date: 1993
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