Harmonic Moments and Large Deviations for a Critical Galton-Watson Process with State-dependent Immigration
Doudou Li, Yuqing Sheng, Mengjun Sun
2025, v.31, Issue 1, 79-93
ABSTRACT
In this paper, a critical Galton-Watson branching process with state-dependent immigration Z = {Zₙ: n ≥ 0} is considered, where immigration is allowed to enter iff the previous generation was empty. We obtain the convergence rate of the harmonic moments of Zₙ firstly, and then the rate of convergence to zero as n → ∞ of P(|Zₙ₊₁/Zₙ − 1| > ε | Zₙ > 0) (ε > 0) is studied.
Keywords: critical, state-dependent, immigration, harmonic moments, large deviations
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