Galton--Watson Branching Processes in a Random Environment. II: Finite-dimensional Distributions

摘要

Let Z_n be the number of particles at moment n in a branching process in a random environment. Assuming that Z_n is "critical" in a certain sense we prove theorems describing the asymptotic behavior as n → ∞ of the distribution of the vector (Z_([nt_1]), …, Z_([nt_b]), of the number of particles in the process at moments 0 < [nt_1] < … < [nt_b] = n given Z_n > 0.