Реферат: Various limit theorems for the critical Crump-Mode-Jagers process Z(t) with long-living particles (non-extinction probabilities and are equivalent, as t → ∞, where the process are defined, as a number of particles in the entire process with the life-length of more then or equal to t) are discussed. These include asymptotics of non-extinction probabilities, convergence of deviations probabilities for Z(t) (existence of a limit for some functions Ψ1(t) and Ψ3(t)) and joint deviations probabilities for Z(t) and Y(t) - the total number of particles that have been born up to t. It is a summary of some previous works difficult of access.

Библиографическая ссылка: Topchij V.A.
Critical general branching processes with long-living particles
First World Congress Branching Processes 05-12 Sep 1993