Additional aspects of the generalized linear-fractional branching process

Additional aspects of the generalized linear-fractional branching process We derive some additional results on the Bienyamé–Galton–Watson-branching process with $$\theta $$ θ -linear fractional branching mechanism, as studied by Sagitov and Lindo (Branching Processes and Their Applications. Lecture Notes in Statistics—Proceedings, 2016). This includes the explicit expression of the limit laws in both the subcritical cases and the supercritical cases with finite mean, and the long-run behavior of the population size in the critical case, limits laws in the supercritical cases with infinite mean when the $$\theta $$ θ process is either regular or explosive, and results regarding the time to absorption, an expression of the probability law of the $$\theta $$ θ -branching mechanism involving Bell polynomials, and the explicit computation of the stochastic transition matrix of the $$\theta $$ θ process, together with its powers. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Annals of the Institute of Statistical Mathematics Springer Journals

Additional aspects of the generalized linear-fractional branching process

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Publisher
Springer Japan
Copyright
Copyright © 2016 by The Institute of Statistical Mathematics, Tokyo
Subject
Statistics; Statistics, general; Statistics for Business/Economics/Mathematical Finance/Insurance
ISSN
0020-3157
eISSN
1572-9052
D.O.I.
10.1007/s10463-016-0573-x
Publisher site
See Article on Publisher Site

Abstract

We derive some additional results on the Bienyamé–Galton–Watson-branching process with $$\theta $$ θ -linear fractional branching mechanism, as studied by Sagitov and Lindo (Branching Processes and Their Applications. Lecture Notes in Statistics—Proceedings, 2016). This includes the explicit expression of the limit laws in both the subcritical cases and the supercritical cases with finite mean, and the long-run behavior of the population size in the critical case, limits laws in the supercritical cases with infinite mean when the $$\theta $$ θ process is either regular or explosive, and results regarding the time to absorption, an expression of the probability law of the $$\theta $$ θ -branching mechanism involving Bell polynomials, and the explicit computation of the stochastic transition matrix of the $$\theta $$ θ process, together with its powers.

Journal

Annals of the Institute of Statistical MathematicsSpringer Journals

Published: Jul 19, 2016

References

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