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Demonstratio Mathematica

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Volume 47, Issue 1


On The Complete Convergence Of Randomly Weighted Sums Of Random Fields

Agnieszka M. Gdula / Andrzej Krajka
Published Online: 2014-03-07 | DOI: https://doi.org/10.2478/dema-2014-0018


Let {X, n̲ ∊ V ⊆ℕd } be a d-dimensional random field indexed by some subset V of lattice ℕd, which are stochastically dominated by a random variable X. Let {an̲, i̲; n̲, i̲ ∊ V } be a 2d-dimensional random field independent of {Xn̲, n̲ ∊ V} and such that |an̲, i̲| M, n̲, i̲ ∊ V for some constant M. In this paper, we give conditions under which the following series

is convergent for some real t, some fixed p > 0 and all ε > 0. Here |n̲| is used for Πdi=1 ni .

The randomly indexed sums of field {X;n̲ ∊ V } are considered too

Keywords : complete convergence; rate of convergence; sums of random fields; multidimensional index


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About the article

Published Online: 2014-03-07

Published in Print: 2014-03-01

Citation Information: Demonstratio Mathematica, Volume 47, Issue 1, Pages 232–252, ISSN (Online) 2391-4661, ISSN (Print) 0420-1213, DOI: https://doi.org/10.2478/dema-2014-0018.

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