Concentration inequalities for sums of random variables, each having power bounded tails

2019/03/06 by Omelchenko, Oleksii, Bulatov, Andrei A.
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1903.02529

Abstract

In this work we present concentration inequalities for the sum S_n of independent integer-valued not necessary indentically distributed random variables, where each variable has tail function that can be bounded by some power function with exponent -α. We show that when 01, then the sum S_n is concentrated around its mean. Since the r.vs. that constitute the sum has tails, which can be bounded by some power function, it follows that results of this paper are applicable to a wide range of different distributions, including the exponentially decaying ones.

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