The Infona portal uses cookies, i.e. strings of text saved by a browser on the user's device. The portal can access those files and use them to remember the user's data, such as their chosen settings (screen view, interface language, etc.), or their login data. By using the Infona portal the user accepts automatic saving and using this information for portal operation purposes. More information on the subject can be found in the Privacy Policy and Terms of Service. By closing this window the user confirms that they have read the information on cookie usage, and they accept the privacy policy and the way cookies are used by the portal. You can change the cookie settings in your browser.
In the paper, we present some Baum–Katz type results for $${\varphi}$$ -mixing random variables with different distributions. Partial results generalize the corresponding one of Shao (Acta Math Sin 31(6):736–747, 1988). In addition, the Marcinkiewicz strong law of large numbers for $${\varphi}$$ -mixing random variables with different distributions is obtained.
Let {Xni, i ≥ 1, n ≥ 1} be an array of rowwise negatively orthant dependent random variables. Some sufficient conditions for complete convergence for arrays of rowwise negatively orthant dependent random variables are presented without assumptions of identical distribution. As an application, the Marcinkiewicz–Zygmund type strong law of large numbers for weighted sums of negatively orthant dependent...
Some exponential probability inequalities for widely negative orthant dependent (WNOD, in short) random variables are established, which can be treated as very important roles to prove the strong law of large numbers among others in probability theory and mathematical statistics. By using the exponential probability inequalities, we study the complete convergence for arrays of rowwise WNOD random...
In this paper, the equivalent conditions of complete moment convergence of the maximum partial weighted sums for negatively superadditive dependent (NSD) random variables are established without the assumption of identical distribution. As applications, the complete moment convergence, the complete convergence and strong law of large numbers for NSD random variables are obtained. The results obtained...
Let $$\{X,X_n,n\ge 1\}$$ { X , X n , n ≥ 1 } be a sequence of identically distributed $$\rho ^*$$ ρ ∗ -mixing random variables, $$\{a_{nk}, 1\le k\le n, n\ge 1\}$$ { a n k , 1 ≤ k ≤ n , n ≥ 1 } an array of real numbers with $$\sup _{n\ge 1}n^{-1}\sum ^n_{k=1}|a_{nk}|^\alpha <\infty $$ sup n ≥ 1 n - 1 ∑ k = 1 n | a n k | α < ∞ ...
In this paper, we investigate the complete convergence of moving average process $$\sum \nolimits _{i=-\infty }^{\infty }a_iY_{i+n}, n\ge 1$$ ∑ i = - ∞ ∞ a i Y i + n , n ≥ 1 , where $$\{Y_i,-\infty<i<+\infty \}$$ { Y i , - ∞ < i < + ∞ } is a doubly infinite sequence of random variables and $$\{a_n,-\infty<n<+\infty \}$$ { a n , - ∞ < n...
In this paper, we study the complete f-moment convergence for arrays of rowwise extended negatively dependent (END) random variables. A general result on the complete moment convergence for arrays of rowwise END random variables is established, which generalizes and improves the corresponding ones of Wu et al. (Glasnik Matematički 49(69):447–466, 2014) and Hu et al. (Sankhya A 77(1):1–29, 2015). As...
Set the date range to filter the displayed results. You can set a starting date, ending date or both. You can enter the dates manually or choose them from the calendar.