Mean convergence theorems and weak laws of large numbers for double arrays of random variables

Le Van Thanh

International Journal of Stochastic Analysis, 2006, vol. 2006, 1-15

Abstract:

For a double array of random variables { X m n , m ≥ 1 , n ≥ 1 } , mean convergence theorems and weak laws of large numbers are established. For the mean convergence results, conditions are provided under which ∑ i = 1 k m ∑ j = 1 l n a m n i j ( X i j − E X i j ) → L r 0 ( 0 < r ≤ 2 ) where { a m n i j ; m , n , i , j ≥ 1 } are constants, and { k n , n ≥ 1 } and { l n , n ≥ 1 } are sequences of positive integers. The weak law results provide conditions for ∑ i = 1 T m ∑ j = 1 τ n a m n i j ( X i j − E X i j ) → p 0 to hold where { T m , m ≥ 1 } and { τ n , n ≥ 1 } are sequences of positive integer-valued random variables. The sharpness of the results is illustrated by examples.

Date: 2006
References: Add references at CitEc
Citations:

Downloads: (external link)
http://downloads.hindawi.com/journals/IJSA/2006/049561.pdf (application/pdf)
http://downloads.hindawi.com/journals/IJSA/2006/049561.xml (text/xml)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hin:jnijsa:049561

DOI: 10.1155/JAMSA/2006/49561

Access Statistics for this article

More articles in International Journal of Stochastic Analysis from Hindawi
Bibliographic data for series maintained by Mohamed Abdelhakeem ().