Limit theorems for a supercritical Poisson random indexed branching process

DOI10.1017/JPR.2015.27zbMath1337.60213OpenAlexW2298307621MaRDI QIDQ2804434

Yanhua Zhang, Zhenlong Gao

Publication date: 29 April 2016

Published in: Journal of Applied Probability (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.jap/1457470577

zbMATH Keywords

law of large numberscentral limit theoremlarge deviation principlePoisson processstock pricesmoderate deviation principlerandom indexed branching process

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Strong limit theorems (60F15) Large deviations (60F10) Branching processes (Galton-Watson, birth-and-death, etc.) (60J80) Point processes (e.g., Poisson, Cox, Hawkes processes) (60G55)

Related Items (8)

Large and moderate deviations for a renewal randomly indexed branching process ⋮ Large deviations for Lotka-Nagaev estimator of a randomly indexed branching process ⋮ Berry-Esseen type inequality for a Poisson randomly indexed branching process via Stein's method ⋮ Controlled branching processes with continuous time ⋮ Deviations for martingale convergence of a branching process with random index ⋮ Stochastic averaging principles for multi-valued stochastic differential equations driven by poisson point Processes ⋮ Deviations for jumping times of a branching process indexed by a Poisson process ⋮ Notes on large deviations for branching processes indexed by a Poisson process

Cites Work

• Moments, moderate and large deviations for a branching process in a random environment
• Large deviations for sums indexed by the generations of a Galton-Watson process
• Large deviation rates for branching processes. I: Single type case
• Critical randomly indexed branching processes
• Stock prices as branching processes
• BARRIER OPTION PRICING BY BRANCHING PROCESSES
• Stock prices as branching processes in random environments: estimation
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