Branching processes with immigration and related topics
نویسنده
چکیده
This is a survey on recent progresses in the study of branching processes with immigration, generalized Ornstein-Uhlenbeck processes and affine Markov processes. We mainly focus on the applications of skew convolution semigroups and the connections in those processes.
منابع مشابه
A limit theorem of discrete Galton - Watson branching processes with immigration 1
We provide a simple set of sufficient conditions for the weak convergence of discrete Galton-Watson branching processes with immigration to continuous time and continuous state branching processes with immigration. Mathematics Subject Classification (2000): 60J80
متن کاملA Limit Theorem for Discrete Galton–watson Branching Processes with Immigration
Weprovide a simple set of sufficient conditions for theweak convergence of discrete-time, discrete-state Galton–Watson branching processes with immigration to continuous-time, continuous-state branching processes with immigration.
متن کاملLimit Theorems for Subcritical Age-dependent Branching Processes with Two Types of Immigration
For the classical subcritical age-dependent branching process the effect of the following two-type immigration pattern is studied. At a sequence of renewal epochs a random number of immigrants enters the population. Each subpopulation stemming from one of these immigrants or one of the ancestors is revived by new immigrants and their offspring whenever it dies out, possibly after an additional ...
متن کاملMaximum family size in branching processes with state
The number W n of oospring of the most proliic particle in the n-th generation of a simple branching process with state-dependent immigration is studied. Limit theorems for W n and EW n are proved. The results are obtained by combining the methods of 8] with known behavior of the population size in branching processes with state{dependent immigration.
متن کاملLimit Theorems for Supercritical Markov Branching Processes with Non-homogeneous Poisson Immigration
This paper deals with Markov branching processes allowing immigration at random time points described by a non-homogeneous Poisson process. This class of processes generalizes a classical model proposed by Sevastyanov, which included a time-homogeneous Poisson immigration. The proposed model finds applications in cell kinetics studies. Limit theorems are obtained in the supercritical case. Some...
متن کامل