Related papers: Population Processes with Immigration
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…
Existing theories of migration either focus on micro- or macroscopic behavior of populations; that is, either the average behavior of entire population is modeled directly, or decisions of individuals are modeled directly. In this work, we…
We study the extremes of branching random walks under the assumption that the underlying Galton-Watson tree has infinite progeny mean. It is assumed that the displacements are either regularly varying or they have lighter tails. In the…
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 this paper we study some mathematical models describing evolution of population density and spread of epidemics in population systems in which spatial movement of individuals depends only on the departure and arrival locations and does…
Birth-and-death processes are widely used to model the development of biological populations. Although they are relatively simple models, their parameters can be challenging to estimate, because the likelihood can become numerically…
We provide a generalization of Theorem 1 in Bartkiewicz, Jakubowski, Mikosch and Wintenberger (2011) in the sense that we give sufficient conditions for weak convergence of finite dimensional distributions of the partial sum processes of a…
This paper introduces stochastic processes that describe the evolution of systems of particles in which particles immigrate according to a Poisson measure and split according to a self-similar fragmentation. Criteria for existence and…
Branching processes $(Z_n)_{n \ge 0}$ in a varying environment generalize the Galton-Watson process, in that they allow time-dependence of the offspring distribution. Our main results concern general criteria for a.s. extinction,…
We consider stochastic dynamics of a population which starts from a small colony on a habitat with large but limited carrying capacity. A common heuristics suggests that such population grows initially as a Galton-Watson branching process…
This work provides a brief introduction to continuous-state branching processes (CB-processes) and continuous-state branching processes with immigration (CBI-processes) accessible to graduate students with reasonable background in…
We consider the setting of either a general non-local branching particle process or a general non-local superprocess, in both cases, with and without immigration. Under the assumption that the mean semigroup has a Perron-Frobenious type…
Reinforced Galton--Watson processes describe the dynamics of a population where reproduction events are reinforced, in the sense that offspring numbers of forebears can be repeated randomly by descendants. More specifically, the evolution…
In this paper we extend two limit theorems which were recently obtained for fragmentation processes to such processes with immigration. More precisely, in the setting with immigration we consider a limit theorem for the process counted with…
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 consider a subcritical branching process in an i.i.d. random environment, in which one immigrant arrives at each generation. We consider the event $% \mathcal{A}_{i}(n)$ that all individuals alive at time $n$ are offspring of the…
We consider a multi-type Galton-Watson branching processes, where the largest in magnitude positive eigenvalue $\rho$ of the first moments matrix is close to unity. Specifically, we examine the random vector representing the number of…
In this paper, we study the Galton-Watson process in the random environment for the particular case when the number of the offsprings in each generation has the fractional linear generation function with random parameters. In this case, the…
In this paper we analyze a branching process with immigration defined recursively by $X_t=\theta_t\circ X_{t-1}+B_t$ for a sequence $(B_t)$ of i.i.d. random variables and random mappings $ \theta_t\circ x:=\theta_t(x)=\sum_{i=1}^xA_i^{(t)},…
A population genetics model based on a multitype branching process, or equivalently a Galton-Watson branching process for multiple alleles, is pre- sented. The diffusion limit forward Kolmogorov equation is derived for the case of neutral…