The Annals of Probability

Doob, Ignatov and optional skipping

Gordon Simons, Lijian Yang, and Yi-Ching Yao

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Abstract

A general set of distribution-free conditions is described under which an i.i.d. sequence of random variables is preserved under optional skipping. This work is motivated by theorems of J. L. Doob and Z. Ignatov, unifying and extending aspects of both.

Article information

Source
Ann. Probab., Volume 30, Number 4 (2002), 1933-1958.

Dates
First available in Project Euclid: 10 December 2002

Permanent link to this document
https://projecteuclid.org/euclid.aop/1039548377

Digital Object Identifier
doi:10.1214/aop/1039548377

Mathematical Reviews number (MathSciNet)
MR1944011

Zentralblatt MATH identifier
1040.60034

Subjects
Primary: 60G40: Stopping times; optimal stopping problems; gambling theory [See also 62L15, 91A60] 28D05: Measure-preserving transformations

Keywords
Ignatov's theorem indexical stopping times disentangled stopping times records $k$-records optional skipping

Citation

Simons, Gordon; Yao, Yi-Ching; Yang, Lijian. Doob, Ignatov and optional skipping. Ann. Probab. 30 (2002), no. 4, 1933--1958. doi:10.1214/aop/1039548377. https://projecteuclid.org/euclid.aop/1039548377


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References

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  • CHAPEL HILL, NORTH CAROLINA 27599-3260 E-MAIL: simons@stat.unc.edu Y.-C. YAO INSTITUTE OF STATISTICAL SCIENCE ACADEMIA SINICA TAIPEI TAIWAN E-MAIL: yao@stat.sinica.edu.tw L. YANG DEPARTMENT OF STATISTICS MICHIGAN STATE UNIVERSITY
  • EAST LANSING, MICHIGAN 48824 E-MAIL: yang@stt.msu.edu