Population Processes with Immigration

Han D.; S. Molchanov; Whitmeyer J.

doi:10.1007/978-3-319-65313-6_16

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June 5, 2026

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Scientists from HSE University–Nizhny Novgorod and the Institute of Physics Belgrade, Serbia, are jointly exploring the application of machine learning techniques and neural networks to the study of nonlinear dynamics. Natalya Stankevich, Leading Research Fellow at the Laboratory of Topological Methods in Dynamics of the Faculty of Informatics, Mathematics, and Computer Science at HSE University–Nizhny Novgorod, spoke to the HSE News Service about this international project.

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Publications

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Population Processes with Immigration

P. 411–434.

Han D., Molchanov S., Whitmeyer J.

The paper contains a complete analysis of the Galton–Watson models with immigration, including the processes in the random environment, stationary or nonstationary ones. We also study the branching random walk on $Z^d$ with immigration and prove the existence of the limits for the first two correlation functions.

Keywords: случайная среда branching process Galton-Watson process Immigration Random environment процесс Гальтона-Ватсона ветвящийся процесс

Publication based on the results of:

Вероятностные и статистические методы анализа сложных моделей, задаваемых стохастическими дифференциальными и разностными уравнениями (2017)

In book

Modern problems of stochastic analysis and statistics - Selected contributions in honor of Valentin Konakov

Heidelberg: Springer, 2017.

Multichannel queueing system in a random environment

Tkachenko A., Moscow University Mathematics Bulletin 2014 Vol. 69 No. 1 P. 37–40

This paper is focused on a multichannel queueing system with heterogeneous servers and regenerative input flow operating in a random environment. The environment can destroy the whole system and the system is reconstructed after that. The necessary and sufficient ergodicity condition is obtained for the system. ...

Added: August 20, 2014