Convergence rate in precise asymptotics for Davis law of large numbers

2015/07/23 by Lingtao Kong, Kong, Lingtao
Mathematics · #60F15 #60G50 #FOS: Mathematics #Probability (math.PR) #math.PR #msc:60F15 #msc:60G50

paper · pdf · doi:10.48550/arxiv.1507.06406

8 pages

arxiv created 2015/07/23 · arxiv updated 2015/07/24

Abstract

Let \X_n,n≥ 1\ be a sequence of i.i.d. random variables with partial sums \S_n,n≥ 1\. Based on the classical Baum-Katz theorem, a paper by Heyde in 1975 initiated the precise asymptotics for the sum ∑_{n≥ 1}P(|S_n|≥εn) as ε goes to zero. Later, Klesov determined the convergence rate in Heyde's theorem. The aim of this paper is to extend Klesov's result to the precise asymptotics for Davis law of large numbers, a theorem in Gut and Spătaru [2000a].

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