Abstract:
We prove local and integral limit theorems for large deviations of Cramer type
for a critical Galton–Watson branching process under the assumption that
the radius of convergence of the generating function of the progeny is
strictly greater than one. The proof is based on a modified Cramer approach
which consists of construction of an auxiliary non-homogeneous in time branching process. This research was supported by the Russian Foundation for Basic Research,
grant 02–01–01252, and by INTAS, grants 99–01317, 00–265.