Some strong limit theorems of weighted sums for negatively dependent generalized Gaussian random variables

Convergence of series of dependent φ-subgaussian random variables

“…Our results are more general and different from the results of Amini et al [1] since we do not need the assumption that a particular conditional expectation of the considered random variables is equal to zero, as it is required in Amini et al [1]. Our results are different from the results of Amini et al [2] since we consider the wider class of ϕ-subgaussian random variables.…”

“…The main results are two theorems presented in Section 3. In Section 4 we give applications to the case of negatively dependent random variables and show how our statements are related to those in Amini et al [1,2] in the special case of classical subgaussian random variables; this type of variables is also discussed in Section 5, where we mainly consider the case of m-dependent random variables and show that our results are stronger than those in Ouy [17]. In Section 6 we present other corollaries.…”

“…There are three more papers that are closely related to our investigation: Ouy [17] and Amini et al [1,2]. First of all, we point out that our results are more general than all of the above quoted papers since we consider the wider class of ϕ-subgaussian random variables.…”

“…In this paper more accurate estimation of subgaussian standard is obtained than in the paper Ouy [17]. In the papers [1] and [2] the case of negatively dependent subgaussian random variables is considered. Our results are more general and different from the results of Amini et al [1] since we do not need the assumption that a particular conditional expectation of the considered random variables is equal to zero, as it is required in Amini et al [1].…”

Some strong limit theorems for arrays of rowwise negatively orthant-dependent random variables

“…A number of limit theorems for NOD random variables have been established by many authors. We refer to Volodin [4] for the Kolmogorov exponential inequality, Asadian et al [5] for the Rosental's-type inequality, Amini et al [6,7], Klesov et al [8], and Li et al [9] for almost sure convergence, Amini and Bozorgnia [10,11], Kuczmaszewska [12], Taylor et al [13], Zarei and Jabbari [14] and Wu [15] for complete convergence, and so on.…”