Sentence examples for for complete convergence from inspiring English sources

For complete convergence and complete moment convergence, there are few reports under sub-linear expectations.

We give some sufficient conditions for complete convergence for weighted sums of arrays of rowwise ρ ˜ -mixing random variables without assumption of identical distribution.

We will give some sufficient conditions for complete convergence for an array of rowwise pairwise NQD random variables without assumption of identical distribution.

Some sufficient conditions for complete convergence for weighted sums of arrays of rowwise ρ ˜ -mixing random variables are presented without assumptions of identical distribution.

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.

Some sufficient conditions for complete convergence for maximal weighted sums max 1 ≤ j ≤ n | ∑ k = 1 j a n k X n k | and weighted sums ∑ k = 1 n a n k X n k are presented, where { X n k, 1 ≤ k ≤ n, n ≥ 1 } is an array of rowwise ψ-mixing random variables, and { a n k, 1 ≤ k ≤ n, n ≥ 1 } is an array of constants.

It provides an improvement of complete convergence for negatively associated random variables by Kuczmaszewska [1] and conditions for complete moment convergence for a nonstationary sequence of negatively associated random variables.

Sufficient and necessary conditions of complete convergence for weighted sums of PNQD random variables are obtained.

The concept of complete convergence for a sequence of random variables was introduced by Hsu and Robbins [1] as follows.

Now let us state some well-known results for the complete convergence of pairwise NQD random variables.

Gut [4] provided necessary and sufficient conditions for the complete convergence of the Cesáro means of i.i.d.i.d