Cesáro summation for random fields

Allan Gut; Ulrich Stadtmueller

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arXiv · 0904.0538

Cesáro summation for random fields

Allan Gut·Ulrich Stadtmueller

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Abstract

Various methods of summation for divergent series of real numbers have been generalized to analogous results for sums of iid random variables. The natural extension of results corresponding to Cesàro summation amounts to proving almost sure convergence of the Cesàro means. In the present paper we extend such results as well as weak laws and results on complete convergence to random fields, more specifically to random variables indexed by $\mathbb{Z}_+^2$, the positive two-dimensional integer lattice points.

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Allan Gut, Ulrich Stadtmueller. 2009-04-03. Cesáro summation for random fields. https://arxiv.org/abs/0904.0538

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