Related papers: Branching processes with immigration and related t…
Skew convolution semigroups play an important role in the study of generalized Mehler semigroups and Ornstein-Uhlenbeck processes. We give a characterization for a general skew convolution semigroup on real separable Hilbert space whose…
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…
In this work we study the long-time behavior for subcritical measure-valued branching processes with immigration on the space of tempered measures. Under some reasonable assumptions on the spatial motion, the branching and immigration…
It is proved that a general non-differentiable skew convolution semigroup associated with a strongly continuous semigroup of linear operators on a real separable Hilbert space can be extended to a differentiable one on the entrance space of…
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 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…
Following the pivotal work of Sevastyanov, who considered branching processes with homogeneous Poisson immigration, much has been done to understand the behaviour of such processes under different types of branching and immigration…
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…
A general affine Markov semigroup is formulated as the convolution of a homogeneous one with a skew convolution semigroup. We provide some sufficient conditions for the regularities of the homogeneous affine semigroup and the skew…
In this paper, a special sequence of controlled branching processes is considered. We provide a simple set of sufficient conditions for the weak convergence of such processes to a weak solution to a kind of continuous branching processes…
In this paper, we investigate the asymptotic behaviors of the critical branching process with immigration $\{Z_n, n\ge 0\}$. First we get some estimation for the probability generating function of $Z_n$. Based on it, we get a large…
This survey aims at collecting and presenting results for one-type, discrete time branching processes with random control functions. In particular, the subclass of critical migration processes with different regimes of immigration and…
This article studies the stability of solutions of equilibrium equations arising in so-called resource dependent branching processes. We argue that these new models, building on the model already presented by Bruss (1984 a), refined and…
A branching process in varying environment with generation-dependent immigration is a modification of the standard branching process in which immigration is allowed and the reproduction and immigration laws may vary over the generations.…
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…
We determine the tail asymptotics of the stationary distribution of a branching process with immigration in a random environment, when the immigration distribution dominates the offspring distribution. The assumptions are the same as in the…
Markov branching systems form a fundamental class of stochastic models that are extensively applied in biology, physics, finance, and other domains. These systems are distinguished by their continuous-time evolution and inherent branching…
The Ornstein-Uhlenbeck (OU) process plays a major role in the analysis of the evolution of phenotypic traits along phylogenies. The standard OU process includes drift and stabilizing selection and assumes that species evolve independently.…
We observe the Galton-Watson Branching Processes. Limit properties of transition functions and their convergence to invariant measures are investigated.