Journal of Applied Probability

Limit theorems for a supercritical Poisson random indexed branching process

Zhenlong Gao and Yanhua Zhang

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Abstract

Let {Zn, n = 0, 1, 2, . . .} be a supercritical branching process, {Nt, t ≥ 0} be a Poisson process independent of {Zn, n = 0, 1, 2, . . .}, then {ZNt, t ≥ 0} is a supercritical Poisson random indexed branching process. We show a law of large numbers, central limit theorem, and large and moderate deviation principles for log ZNt.

Article information

Source
J. Appl. Probab., Volume 53, Number 1 (2016), 307-314.

Dates
First available in Project Euclid: 8 March 2016

Permanent link to this document
https://projecteuclid.org/euclid.jap/1457470577

Mathematical Reviews number (MathSciNet)
MR3471965

Zentralblatt MATH identifier
1337.60213

Subjects
Primary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)
Secondary: 60F10: Large deviations

Keywords
Central limit theorem large deviation principle moderate deviation principle random indexed branching process stock prices

Citation

Gao, Zhenlong; Zhang, Yanhua. Limit theorems for a supercritical Poisson random indexed branching process. J. Appl. Probab. 53 (2016), no. 1, 307--314. https://projecteuclid.org/euclid.jap/1457470577


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