Аннотация:
A multitype indecomposable, nonperiodic,
critical Bellman–Harris branching process is considered. It is assumed that
the types of the process may be splitted into two classes. A particle whose
type belongs to the first class has a finite expected life-length, while the
expected life-length of a particle whose type belongs to the second class is
infinite.
Assuming that the tail of the life-length distribution of a particle with
type from the second class is regularly varying at infinity with parameter
depending on the type, we investigate the asymptotic behavior of the first
and second moments for the number of particles of all types as well as the
increments of the first moments. Our proofs are based on the asymptotic
properties of some renewal matrices defined in terms of certain
characteristics of the initial Bellman–Harris branching process.