Geodesic
Deviations for random sums indexed by the generations of a branching process
Filomat, Tome 35 (2021) no. 10, p. 3303

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DOI

Applying the results about harmonic moments of classical Galton–Watson process, we obtain the deviations for random sums indexed by the generations of a branching process. Our results show that the decay rates of large deviations and moderate deviations depend heavily on the degree of the heavy tail and the asymptotic distributions depend heavily on the normalizing constants. If the underlying Galton– Watson process belongs to the Schröder case, both large deviation and moderate deviation probabilities show three decay rates, where the critical case depends heavily on the Schröder index. Else if the Galton– Watson process belongs to the Böttcher case, there are only two decay rate for both large deviation and moderate deviation probabilities. Simulations are also given to illustrate our results
DOI : 10.2298/FIL2110303Z
Classification : 60J80, 60F10
Keywords: large deviation, moderate deviation, normal deviation, Galton–Watson process, Lotka–Nagaev estimator 
Yanjiao Zhu; Zhenlong Gao. Deviations for random sums indexed by the generations of a branching process. Filomat, Tome 35 (2021) no. 10, p. 3303 . doi: 10.2298/FIL2110303Z
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     author = {Yanjiao Zhu and Zhenlong Gao},
     title = {Deviations for random sums indexed by the generations of a branching process},
     journal = {Filomat},
     pages = {3303 },
     year = {2021},
     volume = {35},
     number = {10},
     doi = {10.2298/FIL2110303Z},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2110303Z/}
}
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