Related papers: Population Processes with Immigration

We investigate the fluctuations around the average density profile in the weakly asymmetric exclusion process with open boundaries in the steady state. We show that these fluctuations are given, in the macroscopic limit, by a centered…

It is a common practice to describe branching random walks in terms of birth, death and walk of particles, which makes it easier to use them in different applications. The main results obtained for the models of symmetric continuous-time…

This paper demonstrates a new regeneration processes technology making use of positive stable distributions. We study the asymptotic behavior of branching processes with a randomly controlled migration component. Using the new method, we…

We propose a class of non-Markov population models with continuous or discrete state space via a limiting procedure involving sequences of rescaled and randomly time-changed Galton--Watson processes. The class includes as specific cases the…

A Galton-Watson process in a varying environment is a discrete time branching process where the offspring distributions vary among generations. It is known that in the critical case, these processes have a Yaglom limit, that is, a suitable…

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…

In this article we focus on the partial sum $S_{n}=X_{1}+\cdots+X_{n}$ of the subcritical branching process with immigration $\{X_{n}\}_{n\in\mathbb{N_{+}}}$, under the condition that one of the offspring $\xi$ or immigration $\eta$ is…

Statistical inference about the speciation process has often been based on the isolation-with-migration (IM) model, especially when the research aim is to learn about the presence or absence of gene flow during divergence. The generalised…

In evolutionary dynamics, well-mixed populations are almost always associated with all-to-all interactions; mathematical models are based on complete graphs. In most cases, these models do not predict fixation probabilities in groups of…

We examine birth--death processes with state dependent transition probabilities and at least one absorbing boundary. In evolution, this describes selection acting on two different types in a finite population where reproductive events occur…

Migrations have played an important role in shaping the genetic diversity of human populations. Understanding genomic data thus requires careful modeling of historical gene flow. Here we consider the effect of relatively recent population…

Let $\{Z_n^i = (Z_n^i(r))_{1 \le r \le d}: n \ge 0\}$ be a supercritical $d$-type branching process in an i.i.d. environment $\xi = (\xi_0, \xi_1, \dots)$, starting from a single particle of type $i$. The offspring distribution at…

We propose a novel class of count time series models alternative to the classic Galton-Watson process with immigration (GWI) and Bernoulli offspring. A new offspring mechanism is developed and its properties are explored. This novel…

Human migration is a type of human mobility, where a trip involves a person moving with the intention of changing their home location. Predicting human migration as accurately as possible is important in city planning applications,…

We establish recurrence and transience criteria for critical branching processes in random environment with immigration. These results are then applied to discuss recurrence and transience of a recurrent random walk in a random environment…

We consider a random walk on a Galton-Watson tree whose offspring distribution has a regular varying tail of order $\kappa\in (1,2)$. We prove the convergence of the renormalised height function of the walk towards the continuous-time…

Let $X_1, X_2,\ldots$ be random elements of the Skorokhod space $D(\mathbb{R})$ and $\xi_1, \xi_2, \ldots$ positive random variables such that the pairs $(X_1,\xi_1), (X_2,\xi_2),\ldots$ are independent and identically distributed. The…

We analyze the stationary tail of a fixed-point equation arising in branching processes with state-independent immigration, when both immigration and offspring distributions have heavy tails with boundary index one. We prove that \[ P(X >…

It is well known that the behaviour of a branching process is completely described by the generating function of the offspring law and its fixed points. Branching random walks are a natural generalization of branching processes: a branching…

We establish a general sufficient condition for a sequence of Galton Watson branching processes in varying environment to converge weakly. This condition extends previous results by allowing offspring distributions to have infinite…