Convergence of Weighted Sums and Laws of Large Numbers in D([0,1]; E)

I. Schiopukratina and P. Daffer

Journal of Multivariate Analysis, 1995, vol. 53, issue 2, 279-292

Abstract: Convergence properties of weighted sums of functions in D([0, 1]; E) (E a Banach space) are investigated. We show that convergence in the Skorokhod J1-topology of a sequence (xn) in D([0, 1]; E) does not imply convergence of a sequence (n) of averages. Convergence in the J1-topology of a sequence (n) of averages is shown, under the growth condition [short parallel] xn [short parallel] [infinity] = o(n), to be equivalent to the convergence of (n) in the uniform topology. Convergence of a sequence (xn,) is shown to imply convergence of the sequence (n) of averages in the M1 and M2 topologies. The strong law of large numbers in D[0, 1] is considered and an example is constructed to show that different definitions of the strong law of large numbers are nonequivalent.

Date: 1995
References: Add references at CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0047-259X(85)71037-8
Full text for ScienceDirect subscribers only

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:eee:jmvana:v:53:y:1995:i:2:p:279-292

Ordering information: This journal article can be ordered from
http://www.elsevier.com/wps/find/supportfaq.cws_home/regional
https://shop.elsevie ... _01_ooc_1&version=01

Access Statistics for this article

Journal of Multivariate Analysis is currently edited by de Leeuw, J.

More articles in Journal of Multivariate Analysis from Elsevier
Bibliographic data for series maintained by Catherine Liu ().