The Annals of Probability

Inequalities for Multitype Branching Processes

Bruce W. Turnbull

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Abstract

Some results of the paper "Inequalities for Branching Processes" [Ann. Prob. 1 (1973)] by the same author are extended to a multitype branching process. Bounds are obtained on the probability of extinction and mean time to extinction of the process when the probability transition laws are allowed to vary from period to period and are required only to belong to some class $\mathscr{M}$.

Article information

Source
Ann. Probab., Volume 1, Number 3 (1973), 475-479.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176996940

Digital Object Identifier
doi:10.1214/aop/1176996940

Mathematical Reviews number (MathSciNet)
MR353478

Zentralblatt MATH identifier
0258.60064

JSTOR
links.jstor.org

Subjects
Primary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)
Secondary: 60G40: Stopping times; optimal stopping problems; gambling theory [See also 62L15, 91A60] 60G45

Keywords
Multitype branching processes Chebyshev-like inequalities gambling theory non-Markovian processes martingales stopping times dynamic programming

Citation

Turnbull, Bruce W. Inequalities for Multitype Branching Processes. Ann. Probab. 1 (1973), no. 3, 475--479. doi:10.1214/aop/1176996940. https://projecteuclid.org/euclid.aop/1176996940


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