Large deviations in the supercritical branching process,

by J.D.Biggins N.H.Bingham

Adv. Appl. Probab. (1993) 25 757-772.

1991 Mathematics Subject Classification: 60J80, 60F10

Abstract

The tail behaviour of the limit of the normalized population size in the simple supercritical branching process, $W$, is studied. Most of the results concern those cases when a tail of the distribution function of $W$ decays exponentially quickly. In essence, knowledge of the behaviour of transforms can be combined with some `large deviation' theory to get detailed information on the oscillation of the distribution function of $W$ near zero or at infinity. In particular we show how an old result of Harris (1948) on the asymptotics of the moment generating function of $W$ translates to tail behaviour.

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