On The Complete Convergence Of Randomly Weighted Sums Of Random Fields

Agnieszka M. Gdula and Andrzej Krajka


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

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