scholarly journals Harmonic moments and large deviations for a critical Galton-Watson process with immigration

2021 ◽  
Author(s):  
Doudou Li ◽  
Mei Zhang
Keyword(s):  
Large Deviations ◽  
Watson Process

scholarly journals How did we get here?

2014 ◽  
Vol 51 (A) ◽  
pp. 63-72
Author(s):  
Kais Hamza ◽  
Fima C. Klebaner
Keyword(s):  
Large Deviations ◽  
Algebraic Equation ◽  
Existence Of Solutions ◽  
Rate Function ◽  
Initial Number ◽  
Watson Process ◽  
Density Process ◽  
Population Numbers

Looking at a large branching population we determine along which path the population that started at 1 at time 0 ended up in B at time N. The result describes the density process, that is, population numbers divided by the initial number K (where K is assumed to be large). The model considered is that of a Galton-Watson process. It is found that in some cases population paths exhibit the strange feature that population numbers go down and then increase. This phenomenon requires further investigation. The technique uses large deviations, and the rate function based on Cramer's theorem is given. It also involves analysis of existence of solutions of a certain algebraic equation.

scholarly journals How did we get here?

2014 ◽  
Vol 51 (A) ◽  
pp. 63-72 ◽  
Author(s):  
Kais Hamza ◽  
Fima C. Klebaner
Keyword(s):  
Large Deviations ◽  
Algebraic Equation ◽  
Existence Of Solutions ◽  
Rate Function ◽  
Initial Number ◽  
Watson Process ◽  
Density Process ◽  
Population Numbers

Looking at a large branching population we determine along which path the population that started at 1 at time 0 ended up inBat timeN. The result describes the density process, that is, population numbers divided by the initial numberK(whereKis assumed to be large). The model considered is that of a Galton-Watson process. It is found that in some cases population paths exhibit the strange feature that population numbers go down and then increase. This phenomenon requires further investigation. The technique uses large deviations, and the rate function based on Cramer's theorem is given. It also involves analysis of existence of solutions of a certain algebraic equation.

scholarly journals Large deviations for Lotka-Nagaev estimator of a randomly indexed branching process

Filomat ◽  
2018 ◽  
Vol 32 (17) ◽  
pp. 5803-5808 ◽  
Author(s):  
Zhenlong Gao ◽  
Lina Qiu
Keyword(s):  
Large Deviations ◽  
Renewal Process ◽  
Continuous Time ◽  
Branching Process ◽  
Asymptotic Properties ◽  
Time Process ◽  
Continuous Time Process ◽  
Watson Process

Consider a continuous time process {Yt=ZNt, t ? 0}, where {Zn} is a supercritical Galton-Watson process and {Nt} is a renewal process which is independent of {Zn}. Firstly, we study the asymptotic properties of the harmonic moments E(Y-rt) of order r > 0 as t ? ?. Then, we obtain the large deviations of the Lotka-Negaev estimator of offspring mean.

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