Almost sure behavior of linear functionals of supercritical branching processes-Reference-Cited by-同舟云学术

Almost sure behavior of linear functionals of supercritical branching processes

Published:1977 Issue:1 Volume:231 Page:233-248
ISSN:0002-9947
Container-title:Transactions of the American Mathematical Society
language:en
Short-container-title:Trans. Amer. Math. Soc.

Author:

Asmussen Søren

Abstract

The exact a.s. behavior of any linear functional Z n ⋅ a {Z_n} \cdot a of a supercritical positively regular p-type ( 1 > p > ∞ ) (1 > p > \infty ) Galton-Watson process { Z n } \{ {Z_n}\} is found under a second moment hypothesis. The main new results are of iterated logarithm type, with normalizing constants depending on the decomposition of a according to the Jordan canonical form of the offspring mean matrix.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/tran/1977-231-01/S0002-9947-1977-0440719-1/S0002-9947-1977-0440719-1.pdf

Reference17 articles.

1. Convergence rates for branching processes;Asmussen, Søren;Ann. Probability,1976

2. Strong limit theorems for general supercritical branching processes with applications to branching diffusions;Asmussen, Søren;Z. Wahrscheinlichkeitstheorie und Verw. Gebiete,1976

3. Limit theorems for multitype continuous time Markov branching processes. I. The case of an eigenvector linear functional;Athreya, Krishna Balasundaram;Z. Wahrscheinlichkeitstheorie und Verw. Gebiete,1969

4. Limit theorems for multitype continuous time Markov branching processes. II. The case of an arbitrary linear functional;Athreya, Krishna Balasundaram;Z. Wahrscheinlichkeitstheorie und Verw. Gebiete,1969

5. Some refinements in the theory of supercritical multitype Markov branching processes;Athreya, Krishna B.;Z. Wahrscheinlichkeitstheorie und Verw. Gebiete,1971

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