Cesáro summation for random fields

Allan Gut, Ulrich Stadtmueller

Published 2009-04-03Version 1

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 Ces\`aro summation amounts to proving almost sure convergence of the Ces\`aro 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.