# zbMATH — the first resource for mathematics

Large deviations in the supercritical branching process. (English) Zbl 0796.60090
Let $$W$$ be the limit of the normed supercritical simple branching process. The functional equation satisfied by the Laplace transform of $$W$$ has been used to obtain properties of the distribution of $$W$$. Detailed study of the left and right hand tails was initiated in a pioneering paper of T. E. Harris [Ann. Math. Stat. 19, 474-494 (1948; Zbl 0041.456)], continued in work of M. S. Dubuc [Z. Wahrscheinlichkeitstheorie Verw. Geb. 19, 281-290 (1971; Zbl 0208.442)], and more recently stimulated by N. H. Bingham [J. Appl. Probab., Spec. Vol. 25A, 215-228 (1988; Zbl 0669.60078)]. The present paper makes further use of existing analytic results to obtain more detailed information about the left and right hand tails, under various conditions on the family size distribution.

##### MSC:
 60J80 Branching processes (Galton-Watson, birth-and-death, etc.) 60F10 Large deviations
##### Citations:
Zbl 0215.256; Zbl 0041.456; Zbl 0208.442; Zbl 0669.60078
Full Text: