A Differential Analog of the Main Lemma of the Theory of Markov Branching Processes and Its Applications
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...
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| Date: | 2005 |
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| Main Authors: | , |
| Format: | Article |
| Language: | Russian English |
| Published: |
Institute of Mathematics, NAS of Ukraine
2005
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/3593 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| Summary: | 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. |
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