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June, 1981 The Geometric Programming Dual to the Extinction Probability Problem in Simple Branching Processes
Paul D. Feigin, Ury Passy
Ann. Probab. 9(3): 498-503 (June, 1981). DOI: 10.1214/aop/1176994422

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.

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Paul D. Feigin. Ury Passy. "The Geometric Programming Dual to the Extinction Probability Problem in Simple Branching Processes." Ann. Probab. 9 (3) 498 - 503, June, 1981. https://doi.org/10.1214/aop/1176994422

Information

Published: June, 1981
First available in Project Euclid: 19 April 2007

zbMATH: 0474.60069
MathSciNet: MR614634
Digital Object Identifier: 10.1214/aop/1176994422

Subjects:
Primary: 60J80

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

Rights: Copyright © 1981 Institute of Mathematical Statistics

Vol.9 • No. 3 • June, 1981
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