The Annals of Probability

The Geometric Programming Dual to the Extinction Probability Problem in Simple Branching Processes

Paul D. Feigin and Ury Passy

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Abstract

It is shown that the well-known problem of determining the probability of extinction in a simple branching process has a duality relation to the problem of determining that offspring distribution which is in a sense closest to the original one and for which the new process is subcritical (or critical). The latter problem is also considered with respect to various measures of distance.

Article information

Source
Ann. Probab., Volume 9, Number 3 (1981), 498-503.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176994422

Digital Object Identifier
doi:10.1214/aop/1176994422

Mathematical Reviews number (MathSciNet)
MR614634

Zentralblatt MATH identifier
0474.60069

JSTOR
links.jstor.org

Subjects
Primary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)

Keywords
Simple branching process extinction probability infinite geometric program geometric duality Kullback directed divergence $\alpha$-entropy branching measure

Citation

Feigin, Paul D.; Passy, Ury. The Geometric Programming Dual to the Extinction Probability Problem in Simple Branching Processes. Ann. Probab. 9 (1981), no. 3, 498--503. doi:10.1214/aop/1176994422. https://projecteuclid.org/euclid.aop/1176994422


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