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

Erkan Nane; Yimin Xiao; Aklilu Zeleke

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arXiv · 1810.10633

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

Erkan Nane·Yimin Xiao·Aklilu Zeleke

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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 \cite{chobanyan-l-s} for a sequence of random variables indexed by a one-parameter.

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BibTeX RIS

Erkan Nane, Yimin Xiao, Aklilu Zeleke. 2018-10-24. Strong laws of large numbers for arrays of random variables and stable random fields. https://arxiv.org/abs/1810.10633

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