  The paper considers the well-known Galton-Watson stochastic branching
process. We are dealing with a non-critical case. In the subcritical case, when
the mean of the direct descendants of one particle per generation of the time
step is less than 1, the population mean of the number of particles on the
positive trajectories of the process stabilizes and approaches 1/K, where K is
the so-called Kolmogorov constant. The paper is devoted to the search for an
explicit expression of this constant depending on the structural parameters of
the process. Our reasoning is essentially based on the Basic Lemma, which
describes the asymptotic expansion of the generating function of the
distribution of the number of particles. An important role is also played by
the asymptotic properties of the transition probabilities of the so-called
Q-process and their property convergence to invariant measures.
