A Differential Analog of the Main Lemma of the Theory of Markov Branching Processes and Its Applications
Abstract
We obtain a differential analog of the main lemma in the theory of Markov branding processes $\mu(t),\quad t \geq 0$, of continuous time. We show that the results obtained can be applied in the proofs of limit theorems in the theory of branching processes by the well-known Stein - Tikhomirov method. In contrast to the classical condition of nondegeneracy of the branching process $\{\mu(t) > 0\}$, we consider the condition of nondegeneracy of the process in distant $\{\mu(\infty) > 0\}$ and justify in terms of generating functions. Under this condition, we study the asymptotic behavior of trajectory of the considered process.
English version (Springer): Ukrainian Mathematical Journal 57 (2005), no. 2, pp 307-315.
Citation Example: Imomov A. A. A Differential Analog of the Main Lemma of the Theory of Markov Branching Processes and Its Applications // Ukr. Mat. Zh. - 2005. - 57, № 2. - pp. 258–264.
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