Abstract
We obtain a differential analog of the main lemma of the theory of Markov branching processes μ(t), t ≥ 0, with continuous time. We show that the results obtained can be used in the proof of limit theorems of the theory of branching processes by the known Stein-Tikhomirov method. Moreover, in contrast to the classical condition of nondegeneracy of the branching process {μ(t) > 0}, we consider the condition of its nondegeneracy in the distant future {μ(∞) > 0} and justify it in terms of generating functions. Under this condition, we study the asymptotic behavior of the trajectory of the process considered.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 57, No. 2, pp. 258–264, February, 2005.
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Imomov, A.A. A Differential Analog of the Main Lemma of the Theory of Markov Branching Processes and Its Applications. Ukr Math J 57, 307–315 (2005). https://doi.org/10.1007/s11253-005-0190-y
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DOI: https://doi.org/10.1007/s11253-005-0190-y