The Hájeck-Rènyi Inequality for the Aana Random Variables and Its Applications

On the strong convergence for weighted sums of asymptotically almost negatively associated random variables

“…A sequence of random variables {X n , n ≥ 1} is called AANA if there exists a nonnegative sequence µ(n) → 0 as n → ∞ such that 6) for all n, k ≥ 1 and for all coordinatewise nondecreasing continuous functions f 1 and f 2 whenever the variances exist.…”

“…For example, Chandra and Ghosal [4], Wang et al [17], Ko et al [6], Yuan and An [22,23], Yuan and Wu [24], Wang et al [13,14,15], Yang et al [18], Hu et al [5], Shen and Wu [7], Tang [10], and so forth. Hence, it is very significant to study limit properties of this wider AANA random variables in probability theory and practical applications.…”

Laws of large numbers for Cesàro alpha-integrable random variables under dependence condition AANA or AQSI

“…The proof of the following lemma is based on certain ideas of Matula [14], Chandra and Ghosal [10], and Ko et al [15].…”

Some Strong Convergence Theorems for Asymptotically almost Negatively Associated Random Variables

“…For recent various results and applications of AANA random variables, we can refer to that Chandra and Ghosal [1] obtained the Kolmogorov type inequality and the strong law of large numbers of Marcinkiewicz-Zygmund; Chandra and Ghosal [2] established the almost sure convergence of weighted averages; Wang et al [10] obtained the law of the iterated logarithm for product sums; Ko et al [5] studied the Hájek-Rényi type inequality; Yuan and An [14] established some Rosenthal type inequalities; Yuan and Wu [15] studied the limiting behavior of the maximum of the partial sum under residual Cesàro alpha-integrability assumption; Wang et al [11,12], Huang et al [3] studied the complete convergence of weighted sums for arrays of rowwise AANA random variables and arrays of rowwise AANA random variables, respectively; Yang et al [16] investigated the complete convergence of moving average process for AANA sequence; and Tang [9] studied the strong law of large numbers for general weighted sums, Shen and Wu [8] …”