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Limit theorems for a supercritical Poisson random indexed branching process

Published online by Cambridge University Press:  24 March 2016

Zhenlong Gao  and
Yanhua Zhang
Zhenlong Gao*
Affiliation:
School of Statistics, Qufu Normal University, Qufu 273165, P. R. China.
Yanhua Zhang
Affiliation:
School of Statistics, Qufu Normal University, Qufu 273165, P. R. China.
*
** Email address: gaozhenlong0325@163.com
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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.

Keywords

Central limit theoremlarge deviation principlemoderate deviation principlerandom indexed branching processstock prices
Type
Short Communications
Information
Journal of Applied Probability , Volume 53 , Issue 1 , March 2016 , pp. 307 - 314
Copyright
Copyright © Applied Probability Trust 2016 

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