Results 31 to 40 of about 137 (132)

Complete convergence of weighted sums under negative dependence

, 2011
Negatively dependent, Complete convergence, Weighted sums, 60F15,
H. Zarei, H. Jabbari
core   +1 more source

Marcinkiewicz‐type strong law of large numbers for double arrays of pairwise independent random variables

International Journal of Mathematics and Mathematical Sciences, Volume 22, Issue 1, Page 171-177, 1999., 1999
Let {Xij} be a double sequence of pairwise independent random variables. If P{|Xmn| ≥ t} ≤ P{|X| ≥ t} for all nonnegative real numbers t and , for 1 < p < 2, then we prove that Under the weak condition of E|X|plog+|X| < ∞, it converges to 0 in L1. And the results can be generalized to an r‐dimensional array of random variables under the conditions ...
Dug Hun Hong, Seok Yoon Hwang
wiley   +1 more source

On complete convergence for randomly indexed sums for a case without identical distributions

International Journal of Mathematics and Mathematical Sciences, Volume 20, Issue 4, Page 773-782, 1997., 1996
In this note we extend the complete convergence for randomly indexed sums given by Klesov (1989) to nonidentical distributed random variables.
Anna Kuczmaszewska, Dominik Szynal
wiley   +1 more source

Limiting behavior of the perturbed empirical distribution functions evaluated at U‐statistics for strongly mixing sequences of random variables

International Journal of Stochastic Analysis, Volume 10, Issue 1, Page 3-20, 1997., 1996
We prove the almost sure representation, a law of the iterated logarithm and an invariance principle for the statistic for a class of strongly mixing sequences of random variables {Xi, i ≥ 1}. Stationarity is not assumed. Here is the perturbed empirical distribution function and Un is a U‐statistic based on X1, …, Xn.
Shan Sun, Ching-Yuan Chiang
wiley   +1 more source

On complete convergence of the sum of a random number of a stable type P random elements

International Journal of Mathematics and Mathematical Sciences, Volume 18, Issue 1, Page 33-36, 1995., 1993
Complete convergence for randomly indexed normalized sums of random elements of the form is established. The random elements {Xn} belong to a type p stable space and are assumed to be independent, but not necessarily identically distributed. No assumptions are placed on the joint distributions of the stopping times {Tn}.
André Adler, Andrey Volodin
wiley   +1 more source

A strong law of large numbers for independent compactly uniformly integrable random sets [PDF]

Arab Journal of Mathematical Sciences
PurposeThe aim of this work is to prove a strong law of large numbers for a sequence of independent compactly uniformly integrable random sets with values in the family of convex closed subsets of a separable Banach space E, again without requiring any ...
Mohammed El Allali, El-Moustafid Mohamed, Fatima Ezzaki   +2 more
doaj   +1 more source

The law of the iterated logarithm for exchangeable random variables

International Journal of Mathematics and Mathematical Sciences, Volume 18, Issue 2, Page 391-396, 1995., 1993
In this note, necessary and sufficient conditions for laws of the iterated logarithm are developed for exchangeable random variables.
Hu-Ming Zhang, Robert L. Taylor
wiley   +1 more source

Strong convergence for weighted sums of (α, β)-mixing random variables and application to simple linear EV regression model

Open Mathematics
In this article, the complete convergence and the Kolmogorov strong law of large numbers for weighted sums of (α,β)\left(\alpha ,\beta )-mixing random variables are presented.
Hu Wenjing, Wang Wei, Wu Yi
doaj   +1 more source

On complete convergence in a Banach space

International Journal of Mathematics and Mathematical Sciences, Volume 17, Issue 1, Page 1-14, 1994., 1993
Sufficient conditions are given under which a sequence of independent random elements taking values in a Banach space satisfy the Hsu and Robbins law of large numbers. The complete convergence of random indexed sums of random elements is also considered.
Anna Kuczmaszewska, Dominik Szynal
wiley   +1 more source

On Feller′s criterion for the law of the iterated logarithm

International Journal of Mathematics and Mathematical Sciences, Volume 17, Issue 2, Page 323-340, 1994., 1993
Combining Feller′s criterion with a non‐uniform estimate result in the context of the Central Limit Theorem for partial sums of independent random variables, we obtain several results on the Law of the Iterated Logarithm. Two of these results refine corresponding results of Wittmann (1985) and Egorov (1971). In addition, these results are compared with
Deli Li, M. Bhaskara Rao, Xiangchen Wang
wiley   +1 more source