On The Complete Convergence Of Randomly Weighted Sums Of Random Fields

Abstract

Let {Xn̲, 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

Keywords

• complete convergence
• rate of convergence
• sums of random fields
• multidimensional index