- Issue
- Journal of Siberian Federal University. Mathematics & Physics. 2021 14 (5)
- Authors
- Imomov, Azam A.
- Contact information
- Imomov, Azam A.: Karshi State University Karshi city, Uzbekistan; https://orcid.org/ 0000-0003-1082-0144
- Keywords
- Markov branching process; generating functions; immigration; transition functions; slowly varying function; invariant measures; convergence rate
- Abstract
The paper discusses the continuous-time Markov Branching Process allowing Immigration. We are considering a critical case for which the second moment of offspring law and the first moment of immigration law are possibly infinite. Assuming that the nonlinear parts of the appropriate generating functions are regularly varying in the sense of Karamata, we prove theorems on convergence of transition functions of the process to invariant measures. We deduce the speed rate of these convergence providing that slowly varying factors are with remainder
- Pages
- 573–583
- DOI
- 10.17516/1997-1397-2021-14-5-573-583
- Paper at repository of SibFU
- https://elib.sfu-kras.ru/handle/2311/143731
Journal of Siberian Federal University. Mathematics & Physics / On Estimation of the Convergence Rate to Invariant Measures in Markov Branching Processes with Possibly Infinite Variance and Allowing Immigration
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