Националният семинар по стохастика

организира съвместна сбирка с

Department of Mathematics (University of Extremadura, Spain)

на 5 май 2021 г. от 15 часа в платформата Zoom.

Доклад на тема

Continuous-time Controlled Branching Processes

ще изнесе

Manuel Molina Fernández (Department of Mathematics and Institute of Advanced  Scientific Computation, University of Extremadura, Spain).

Абстракт: Classical branching processes with independent individual evolutions have been extensively studied in the literature. It is well known that in many real situations, the evolutions of the individuals are not independent. Several approaches to modeling dependent evolutions have been investigated. In particular, controlled branching processes constitute a broad class of integer-valued discrete-time Markov models where the population size in every generation could be randomly regulated before the reproduction by an emigration of a part of the population or after the reproduction by an immigration of individuals. In these processes, the evolutions of the individuals are not independent nevertheless that they reproduce independently of each others. A general definition of a continuous-time controlled branching process does not exist up to now. Recently, with the main motivation to provide some solution on this issue, we have introduced and investigated a new class of continuous-time controlled branching processes. For the critical case, we have established some limiting distributions. An extension of this class as regenerative controlled branching processes with continuous time has been proposed and some asymptotic properties investigated. We have also considered multitype random control functions, we have especially studied a case with three specific control functions (controlled branching processes with random migration). In this talk, a summary about the main results obtained in such research, developed in [1], will be presented.
[1] González, M., Molina, M., del Puerto, I.M., Yanev, G.P., Yanev, N.M. (2021). Controlled
branching processes with continuous time. Journal of Applied Probability, vol. 58, (to appear)..

Участието ще е достъпно чрез линка към  Zoom стаята:

Topic: Национален семинар по стохастика
Time: May 5, 2021 15:00 Sofia

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