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Notes on large deviations for branching processes indexed by a Poisson process

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Abstract

Consider a continuous-time process {ZNt}, where {Zn} is a Galton–Watson process with offspring mean m, and {Nt} is a Poisson process independent of {Zn}. It turns out that Rt := ZNt+1/ZNt is an estimator of m. We deal with large deviation rates for the convergence of Rt to m for the supercritical and critical cases.

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  1. School of Statistics, Qufu Normal University, Qufu, 273165, China

    Zhenlong Gao

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  1. Zhenlong Gao
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Correspondence to Zhenlong Gao.

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Supported by National Natural Science Foundation of China (No. 11601260).

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Gao, Z. Notes on large deviations for branching processes indexed by a Poisson process. Lith Math J 60, 25–28 (2020). https://doi.org/10.1007/s10986-020-09470-0

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  • DOI: https://doi.org/10.1007/s10986-020-09470-0

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