ACTA MATHEMATICA UNIVERSITATIS COMENIANAE

ACTA MATHEMATICA UNIVERSITATIS COMENIANAE

Vol. 65, 1 (1996)
pp. 125-128

THE MODIFICATION OF THE GALTON-WATSON PROCESS
J. KALAS

Abstract. In the paper we study the following modification of the classical Galton-Watson process. We suppose, starting with the first generation, that a particle of some generation ``lives to see'' the time of generating of the random number of new particles with the probability $p$. It is shown that the probability of the destruction of the population is equal to the smallest root of the equation $F(p\cdot s + q) = s$ ($q=1-p$).

AMS subject classification. 60J80
Keywords. Branching process, generating function, the probability of the destruction of the population

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