The National Seminar on Probability and Statistics
is organizing a joint meeting with the
Department of Mathematics (University of Extremadura, Spain)
on May 5, 2021 at 3:00 p.m. (UTC +3) in Zoom.
A talk on:
Continuous-time Controlled Branching Processes
will be delivered by Manuel Molina Fernández (Department of Mathematics and Institute of Advanced Scientific Computation, University of Extremadura, Spain).
Abstract: 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).
Link to the Zoom meeting:
Topic: Национален семинар по стохастика
Time: May 5, 2021 15:00 Sofia
Join Zoom Meeting
https://us02web.zoom.us/j/87083470078?pwd=QmNleWZIUkdheitsK2FMWmFFazNPdz09
Meeting ID: 870 8347 0078
Passcode: 816384
Everybody is invited.