Upper bound for the tail functions of the growth rate for supercritical branching processes in random environment

2019/12/26 by Ye, Yinna
#60G42 #60J80 #60K37 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1912.11790

Abstract

Suppose that (Z_n)_n≥0 is a supercritical branching process in independent and identically distributed random environment. The right tail function of the scaled growth rate for (Z_n)_n≥0 is studied. The upper bounds for ℙ[(log Z_n)/(Mn)-μ≥ x] for any x≥3 are obtained, by applying an extension of the Hoeffding type inequalities.

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