Related papers: Multi-type branching processes with immigration ge…
The paper studies a class of critical Markov branching processes with infinite variance of the offspring distribution. The processes admit also an immigration component at the jump-points of a non-homogeneous Poisson process, assuming that…
The paper studies a class of critical Markov branching processes with infinite variance of the offspring distribution. The processes admit also an immigration component at the jump-points of a non-homogeneous Poisson process, assuming that…
The nonlinear branching process with immigration is constructed as the pathwise unique solution of a stochastic integral equation driven by Poisson ran- dom measures. Some criteria for the regularity, recurrence, ergodicity and strong…
In a multitype branching process, it is assumed that immigrants arrive according to a nonhomogeneous Poisson or a generalized Polya process (both processes are formulated as a nonhomogeneous birth process with an appropriate choice of…
A special type of immigration associated with measure-valued branching processes is formulated by using skew convolution semigroups. We give characterization for a general inhomogeneous skew convolution semigroup in terms of probability…
A family of continuous-state branching processes with immigration are constructed as the solution flow of a stochastic equation system driven by time-space noises. The family can be regarded as an inhomogeneous increasing path-valued…
The current paper focuses on studying the impact of immigration with an infinite mean, driven by a discrete-stable compound Poisson process, when it is entering the branching environment with infinite variance of reproduction. Our goal is…
Multitype branching processes with immigration in one type are used to model the dynamics of stage-structured plant populations. Parametric inference is first carried out when count data of all types are observed. Statistical…
We develop a new methodology for the fluctuation theory of continuous-time skip-free Markov chains, extending the recent work of Choi and Patie [5] for discrete-time skip-free Markov chains. As the main application we use it to derive a…
We study two different types of vector point processes with interacting components, introducing a migration-type effect. The first case concerns two groups which modify their states with rate functions depending on time only. This yields a…
We prove the existence and pathwise uniqueness of the solution to a stochastic integral equation driven by Poisson random measures based on Kuznetsov measures for a continuous-state branching process. That gives a direct construction of the…
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…
We consider a branching process with Poissonian immigration where individuals have inheritable types. At rate theta, new individuals singly enter the total population and start a new population which evolves like a supercritical,…
The paper contains the complete analysis of the Galton-Watson models with immigration, including the processes in the random environment, stationary or non-stationary ones. We also study the branching random walk on $Z^d$ with immigration…
We observe the continuous-time Markov Branching Process without high-order moments and allowing Immigration. Limit properties of transition functions and their convergence to invariant measures are investigated. Main mathematical tool is…
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…
Given a homogeneous Poisson process on ${\mathbb{R}}^d$ with intensity $\lambda$, we prove that it is possible to partition the points into two sets, as a deterministic function of the process, and in an isometry-equivariant way, so that…
A superprocess with dependent spatial motion and interactive immigration is constructed as the pathwise unique solution of a stochastic integral equation carried by a stochastic flow and driven by Poisson processes of one-dimensional…
In this paper the asymptotic behavior of a critical multi-type branching process with immigration is described when the offspring mean matrix is irreducible, in other words, when the process is indecomposable. It is proved that sequences of…
By a random process with immigration at random times we mean a shot noise process with a random response function (response process) in which shots occur at arbitrary random times. The so defined random processes generalize random processes…