Weak laws for dependent sums

William L. Steiger

doi:10.1090/S0002-9939-1973-0319242-2

Weak laws for dependent sums

William L. Steiger

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

A general weak law of large numbers for sums Sn=Xi + -a-+X is proved. That is, without assuming the existence of any moments, and allowing any sort of dependence structure, conditions are given for Sn/n→0 in probability; the conditions are not necessary. However they are sufficient for a much stronger statement, namely that Sv Avn-^Q in probability in many cases where positive, integer-valued random variables j.

Original language	English (US)
Pages (from-to)	278-281
Number of pages	4
Journal	Proceedings of the American Mathematical Society
Volume	41
Issue number	1
DOIs	https://doi.org/10.1090/S0002-9939-1973-0319242-2
State	Published - Nov 1973
Externally published	Yes

All Science Journal Classification (ASJC) codes

General Mathematics
Applied Mathematics

Keywords

Dependent random variables
Random sums
Weak law of large numbers

Access to Document

10.1090/S0002-9939-1973-0319242-2

Cite this

@article{ae0cd64858ec47aabb986a24ef240dae,

title = "Weak laws for dependent sums",

abstract = "A general weak law of large numbers for sums Sn=Xi + -a-+X is proved. That is, without assuming the existence of any moments, and allowing any sort of dependence structure, conditions are given for Sn/n→0 in probability; the conditions are not necessary. However they are sufficient for a much stronger statement, namely that Sv Avn-^Q in probability in many cases where positive, integer-valued random variables j.",

keywords = "Dependent random variables, Random sums, Weak law of large numbers",

author = "Steiger, {William L.}",

year = "1973",

month = nov,

doi = "10.1090/S0002-9939-1973-0319242-2",

language = "English (US)",

volume = "41",

pages = "278--281",

journal = "Proceedings of the American Mathematical Society",

issn = "0002-9939",

publisher = "American Mathematical Society",

number = "1",

}

TY - JOUR

T1 - Weak laws for dependent sums

AU - Steiger, William L.

PY - 1973/11

Y1 - 1973/11

N2 - A general weak law of large numbers for sums Sn=Xi + -a-+X is proved. That is, without assuming the existence of any moments, and allowing any sort of dependence structure, conditions are given for Sn/n→0 in probability; the conditions are not necessary. However they are sufficient for a much stronger statement, namely that Sv Avn-^Q in probability in many cases where positive, integer-valued random variables j.

AB - A general weak law of large numbers for sums Sn=Xi + -a-+X is proved. That is, without assuming the existence of any moments, and allowing any sort of dependence structure, conditions are given for Sn/n→0 in probability; the conditions are not necessary. However they are sufficient for a much stronger statement, namely that Sv Avn-^Q in probability in many cases where positive, integer-valued random variables j.

KW - Dependent random variables

KW - Random sums

KW - Weak law of large numbers

UR - http://www.scopus.com/inward/record.url?scp=84968505371&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84968505371&partnerID=8YFLogxK

U2 - 10.1090/S0002-9939-1973-0319242-2

DO - 10.1090/S0002-9939-1973-0319242-2

M3 - Article

AN - SCOPUS:84968505371

SN - 0002-9939

VL - 41

SP - 278

EP - 281

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

IS - 1

ER -

Weak laws for dependent sums

Abstract

All Science Journal Classification (ASJC) codes

Keywords

Access to Document

Other files and links

Fingerprint

Cite this