Strong laws of large numbers for arrays of random variables and stable random fields

2018/10/24 by Nane, Erkan, Xiao, Yimin, Zeleke, Aklilu
#60F15 #60G60 #FOS: Mathematics #Probability (math.PR) #Statistics Theory (math.ST)

paper · doi:10.48550/arxiv.1810.10633

Abstract

Strong laws of large numbers are established for random fields with weak or strong dependence. These limit theorems are applicable to random fields with heavy-tailed distributions including fractional stable random fields. The conditions for SLLN are described in terms of the p-th moments of the partial sums of the random fields, which are convenient to verify. The main technical tool in this paper is a maximal inequality for the moments of partial sums of random fields that extends the technique of Levental, Chobanyan and Salehi \citechobanyan-l-s for a sequence of random variables indexed by a one-parameter.

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