Related papers: Population Processes with Immigration
We consider a critical branching process $Y_{n}$ in an i.i.d. random environment, in which one immigrant arrives at each generation. Let $% \mathcal{A}_{i}(n)$ be the event that all individuals alive at time $n$ are offspring of the…
We construct two kinds of stochastic flows of discrete Galton-Watson branching processes. Some scaling limit theorems for the flows are proved, which lead to local and nonlocal branching superprocesses over the positive half line.
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…
Branching processes and Fleming-Viot processes are two main models in stochastic population theory. Incorporating an immigration in both models, we generalize the results of Shiga (1990) and Birkner et al. (2005) which respectively connect…
Under natural assumptions, a Feller type diffusion approximation is derived for critical, irreducible multi-type continuous state and continuous time branching processes with immigration. Namely, it is proved that a sequence of…
Near critical catalyst-reactant branching processes with controlled immigration are studied. The reactant population evolves according to a branching process whose branching rate is proportional to the total mass of the catalyst. The bulk…
A model is proposed and studied describing an infinite population of point migrants arriving in and departing from $X\subseteq \mathbf{R}^d$, $d\geq 1$. Both these acts occur at random with state-dependent rates. That is, depending on their…
A properly scaled critical Galton-Watson process converges to a continuous state critical branching process $\xi(\cdot)$ as the number of initial individuals tends to infinity. We extend this classical result by allowing for overlapping…
Lattice-based random walk models are widely used to study populations of migrating cells with motility bias and proliferation. Crowding is typically represented by volume exclusion, where each lattice site can be occupied by at most one…
Functional limit theorems are established for continuous-state branching processes with immigration (CBIs), where the reproduction laws have finite first moments and the immigration laws exhibit large tails. Different regimes of immigration…
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…
A general multi-type population model is considered, where individuals live and reproduce according to their age and type, but also under the influence of the size and composition of the entire population. We describe the dynamics of the…
In this paper, we firstly give a reconstruction for Crump-Mode-Jagers processes with immigration as solutions to a class of stochastic Volterra integral equations, which offers us a new insight for the evolution dynamics of age-dependent…
We focus on the partial sum $S_{n}=X_{1}+\cdots+X_{n}$ of the critical branching process with immigration $\{X_{n}\}$, when the offspring $\xi$ is regularly varying with index $\nu+1$ and the immigration $\eta$ is regularly varying with…
The entropy rates of the Wright-Fisher process, the Moran process, and generalizations are computed and used to compare these processes and their dependence on standard evolutionary parameters. Entropy rates are measures of the variation…
We study the long-term behavior of weighted multi-type branching processes, focusing on extending classical laws of large numbers and martingale convergence to settings with infinitely many weighted particles, arbitrary type spaces and…
We consider random walks in dynamic random environments, with an environment generated by the time-reversal of a Markov process from the oriented percolation universality class. If the influence of the random medium on the walk is small in…
Density dependent Markov population processes with countably many types can often be well approximated over finite time intervals by the solution of the differential equations that describe their average drift, provided that the total…
In this paper, we study a Galton-Watson process $(Z_n)$ with infinitely many types in a random ergodic environment $\bar{\xi}=(\xi_n)_{n\geq 0}$. We focus on the supercritical regime of the process, where the quenched average of the size of…
The Galton-Watson process is a model for population growth which assumes that individuals reproduce independently according to the same offspring distribution. Inference usually focuses on the offspring average as it allows to classify the…