The explicit expression for the Kolmogorov constant given in Theorem 1.2 of [1] has a restricted range of validity: it gives the constant precisely for linear-fractional offspring generating functions, whereas for other subcritical offspring generating functions the constant may be strictly larger or strictly smaller than that expression. Within the class of embeddable offspring generating functions the expression is a sharp lower bound for the constant.

Recent investigations have argued that there is a simple explicit representation for the Kolmogorov constant c associated with the subcritical Galton–Watson branching process. We exhibit examples showing that although this representation can be valid, it more often is not. Our work is presented in terms of the limiting conditional mean population size $\mu=c^{-1}$. The analogous quantity for the Markov branching process is denoted by $\widehat\mu$. We show that the simple representation put forward for $\widehat\mu$ in fact is an upper bound that is attained only if the offspring-number probability-generating function is quadratic. The conditional mean $\mu$ is the limit of a computable increasing sequence $(\mu_n$). Estimates of n are determined ensuring that, for any small positive number $\varepsilon$, $0\lt\mu-\mu_n\le \varepsilon$.

We consider a discrete-time population growth system called the Bienaymé–Galton–Watson stochastic branching system. We deal with a noncritical case, in which the per capita offspring mean $m\neq1$. The famous Kolmogorov theorem asserts that the expectation of the population size in the subcritical case $m<1$ on positive trajectories of the system asymptotically stabilizes and approaches ${1}/\mathcal{K}$, where $\mathcal{K}$ is called the Kolmogorov constant. The paper is devoted to the search for an explicit expression of this constant depending on the structural parameters of the system. Our argumentation is essentially based on the basic lemma describing the asymptotic expansion of the probability-generating function of the number of individuals. We state this lemma for the noncritical case. Subsequently, we find an extended analogue of the Kolmogorov constant in the noncritical case. An important role in our discussion is also played by the asymptotic properties of transition probabilities of the Q-process and their convergence to invariant measures. Obtaining the explicit form of the extended Kolmogorov constant, we refine several limit theorems of the theory of noncritical branching systems, showing explicit leading terms in the asymptotic expansions.