The Annals of Probability

A Renewal Theorem for an Urn Model

Pranab Kumar Sen

Full-text: Open access

Abstract

For an urn model (arising typically in the sequential estimation of the size of a finite population), along with an invariance principle for a partial sequence of nonnegative random variables, a renewal theorem relating to some stopping times is established. A representation of these random variables in terms of linear combinations of some martingale-differences provides the key to a simple solution.

Article information

Source
Ann. Probab., Volume 10, Number 3 (1982), 838-843.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176993794

Digital Object Identifier
doi:10.1214/aop/1176993794

Mathematical Reviews number (MathSciNet)
MR659553

Zentralblatt MATH identifier
0544.60042

JSTOR
links.jstor.org

Subjects
Primary: 60F17: Functional limit theorems; invariance principles
Secondary: 60G40: Stopping times; optimal stopping problems; gambling theory [See also 62L15, 91A60] 62L99: None of the above, but in this section

Keywords
Finite population size invariance principles martingale-differences renewal theorem sequential estimation stopping time urn model

Citation

Sen, Pranab Kumar. A Renewal Theorem for an Urn Model. Ann. Probab. 10 (1982), no. 3, 838--843. doi:10.1214/aop/1176993794. https://projecteuclid.org/euclid.aop/1176993794


Export citation