Convergence of series of dependent φ-subgaussian random variables

Abstract

The almost sure convergence of weighted sums of ϕ-subgaussian m-acceptable random variables is investigated. As corollaries, the main results are applied to the case of negatively dependent and m-dependent subgaussian random variables. Finally, an application to random Fourier series is presented.

Convergence of series of strongly integrable random variables and applications

“…In section 4 the problem of convergence of the series S(ã, X ) is considered assuming that X is a d-subgaussian increments sequence. This framework enables us to deduce corresponding results for series of independent or negatively dependent increments and for conditionally subgaussian series, we thus recover some results of [1,2,3,6,9]. Finally, we examine an example of a d-subgaussian series, which is beyond the scope of the last quoted papers.…”

“…These results were extended to m-dependent subgaussian random variables by Ouy [16] and to negatively dependent subgaussian random variables by Amini et al [1,2]. More recently Guiliano et al [9] examined the convergence of the series S(ã, X ) when X is an m-acceptable sequence of φ-subgaussian random variables, they obtained positive results assuming that x → φ(|x| 1/p ) is a convex function for some p ∈ [1,2], then they deduced the corresponding results for the classical subgaussian case.…”

Some exponential inequalities for acceptable random variables and complete convergence

“…As is mentioned in Giuliano et al [4], a sequence of NOD random variables with a finite Laplace transform or finite moment generating function near zero (and hence a sequence of NA random variables with finite Laplace transform, too) provides us an example of acceptable random variables. For example, Xing et al [6] consider a strictly stationary NA sequence of random variables.…”

A Bound for Norms in Lp(T) of Deviations of φ-sub-Gaussian Stochastic Processes

“…General theory and various applications of sub-Gaussian, ϕ-sub-Gaussian, and strictly ϕ-sub-Gaussian random variables and processes can be found in the book of Buldygin and Kozachenko [1] and in the papers [2,4,5,7,8,9,12,13,14].…”