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Moment computations for subcritical branching processes

Published online by Cambridge University Press:  14 July 2016

Kenneth Lange,
Michael Boehnke and
Richard Carson
Kenneth Lange*
Affiliation:
University of California, Los Angeles
Michael Boehnke*
Affiliation:
University of California, Los Angeles
Richard Carson*
Affiliation:
University of California, Los Angeles
*
∗ Postal address: Department of Biomathematics, University of California, Los Angeles, CA 90024, U.S.A.
∗ Postal address: Department of Biomathematics, University of California, Los Angeles, CA 90024, U.S.A.
∗ Postal address: Department of Biomathematics, University of California, Los Angeles, CA 90024, U.S.A.
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Abstract

The present paper considers methods for computing moments connected with subcritical multitype branching processes. By stressing the interplay between moment and cumulant structure, it is possible to prove simultaneously the existence of the moments. The kinds of moments considered are those arising in (1) times to extinction, (2) ultimate numbers of particles starting from a single particle, and (3) equilibrium numbers of particles for subcritical processes experiencing immigration.

Keywords

SUBCRITICAL MULTITYPE BRANCHING PROCESSMOMENTCUMULANTCOMPUTATION

Information

Type
Research Papers
Information
Journal of Applied Probability , Volume 18 , Issue 1 , March 1981, pp. 52 - 64
Copyright
Copyright © Applied Probability Trust 

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Footnotes

Research supported in part by the University of California, Los Angeles; NIH Research Career Development Grant K04 HD00307; and NRSA Training Grant GM 7191.

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