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On the left tail asymptotics for the limit law of supercritical Galton–Watson processes in the Böttcher case

Klaus FleischmannVitali Wachtel — 2009

Annales de l'I.H.P. Probabilités et statistiques

Under a well-known scaling, supercritical Galton–Watson processes converge to a non-degenerate non-negative random limit variable . We are dealing with the left tail (i.e. close to the origin) asymptotics of its law. In the Böttcher case (i.e. if always at least two offspring are born), we describe the precise asymptotics exposing oscillations (Theorem 1). Under a reasonable additional assumption, the oscillations disappear (Corollary 2). Also in the Böttcher case, we improve a recent lower deviation...

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