On The Complete Convergence Of Randomly Weighted Sums Of Random Fields

Demonstratio mathematica

article

Agnieszka M. Gdula ; Andrzej Krajka

关键词: complete convergence;    rate of convergence;    sums of random fields;    multidimensional index;   

DOI  :  10.2478/dema-2014-0018

学科分类：外科医学

来源: De Gruyter

【 摘 要 】

Let {X n̲ , n̲ ∊ V ⊆ℕ d } be a d-dimensional random field indexed by some subset V of lattice ℕ d , which are stochastically dominated by a random variable X. Let {a n̲, i̲ ; n̲, i̲ ∊ V } be a 2d-dimensional random field independent of {X n̲, n̲ ∊ V} and such that |a n̲, 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 Π d i=1 n i . The randomly indexed sums of field {X n̲ ;n̲ ∊ V } are considered too.

【 授权许可】

CC BY