Related papers: Numerical Aspects of Computing Possible Equilibria…
The objective of this article is to create a framework to study asymptotic equilibria in human populations with a special focus on immigration. We present a new model, based on Resource Dependent Branching Processes, which is now broad…
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.…
We study a dynamic model of ecosystems where immigration plays an essential role both in assembling the species community and in mantaining its biodiversity. This framework is particularly relevant for insular ecosystems. Population…
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…
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…
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…
Guided by the relationship between the breadth-first walk of a rooted tree and its sequence of generation sizes, we are able to include immigration in the Lamperti representation of continuous-state branching processes. We provide a…
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…
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…
We consider a stationary continuous model of random size population with non-neutral mutations using a continuous state branching process with non-homogeneous immigration. We assume the type (or mutation) of the immigrants is random given…
We formulate an age-structured nonlinear partial differential equation model that features short-term immigration effects in a population. Individuals can immigrate into the population as any of the three stages in the model: susceptible,…
This paper deals into the long-term behavior of subordinated critical branching processes with migration. We focus on scenarios where emigration is the dominant factor and introduce additional randomness in timing through a subordination…
Life is on the razor's edge as resulting from competitive birth and death random forces. We illustrate this aphorism in the context of three Markov chain population models where systematic random immigration events promoting growth are…
In this paper we consider a triangular array of branching processes with non-stationary immigration. We prove a weak convergence of properly normalized branching processes with immigration to deterministic function under assumption that…
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…
We consider a class of physiologically structured population models, a first order nonlinear partial differential equation equipped with a nonlocal boundary condition, with a constant external inflow of individuals. We prove that the…
This paper presents a quantitative framework for forecasting immigrant integration using immigrant density as the single driver. By comparing forecasted integration estimates based on data collected up to specific periods in time, with…
In this paper, we study continuous-state interacting multi-type branching processes with immigration (CIMBI processes), where inter-specific interactions -- whether competitive, cooperative, or of a mixed type -- are proportional to the…
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…
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…