We prove limit theorems for a family of random vectors whose coordinates are a special form of random sums of Bernoulli random variables. Applying these limit theorems, we study the number ofâ€¦ (More)

The number Yn of oospring of the most proliic individual in the nth generation of a Bienaym e-Galton-Watson process is studied. The asymptotic behavior of Yn as n ! 1 may be viewed as an extremeâ€¦ (More)

In the paper a method for investigation of some functionals of branching stochastic processes related to their genealogy will be discussed. The method is based on the construction and study of aâ€¦ (More)

Let Z(Ï„, t) is the number of individuals at time Ï„ having more than Î¸(t âˆ’ Ï„) descendants at time t, t > Ï„. Here Î¸(t) is some non-negative function. Limit distributions for Z(Ï„, t) when populationâ€¦ (More)