Related papers: Branching processes in varying environment with ge…
We study a repulsion-diffusion equation with immigration, whose asymptotic behaviour is related to stability of long-term dynamics in spatial population models and other branching particle systems. We prove well-posedness and find sharp…
We study a class of evolution models, where the breeding process involves an arbitrary exchangeable process, allowing for mutations to appear. The population size $n$ is fixed, hence after breeding, selection is applied. Individuals are…
I study a population model in which the reproduction rate lambda is inherited with mutation, favoring fast reproducers in the short term, but conflicting with a process that eliminates agglomerations of individuals. The model is a variant…
The aim of this paper is to introduce a multitype branching process with random migration following the research initiated with the Galton-Watson process with migration introduced in [Yanev & Mitov (1980) C. R. Acad. Bulg. Sci.…
Let $\{Y_{n}$, $n \geq 1\}$ be a critical branching process with immigration having finite variance for the offspring number of particles and finite mean for the immigrating number of particles. In this paper, we study lower deviation…
Ancestral inference for branching processes in random environments involves determining the ancestor distribution parameters using the population sizes of descendant generations. In this paper, we introduce a new methodology for ancestral…
We consider a supercritical branching process and define a contact tracing mechanism on its genealogical tree. We calculate the growth rate of the post tracing process, and give conditions under which the tracing is strong enough to drive…
In this article we provide a sufficient condition for a continuous-state branching process with immigration (CBI process) to not hit its boundary, i.e. for non-extinction. Our result applies to arbitrary dimension $d \geq 1$ and is…
Consider a multi-dimensional supercritical branching process with offspring distribution in a parametric family. Here, each vector coordinate corresponds to the number of offspring of a given type. The process is observed under family-size…
By a random process with immigration at random times we mean a shot noise process with a random response function (response process) in which shots occur at arbitrary random times. The so defined random processes generalize random processes…
We consider an extended birth-death-immigration process defined on a lattice formed by the integers of $d$ semiaxes joined at the origin. When the process reaches the origin, then it may jumps toward any semiaxis with the same rate. The…
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…
In the present paper, we characterize the behavior of supercritical branching processes in random environment with linear fractional offspring distributions, conditioned on having small, but positive values at some large generation. As it…
Using the annealed approach we investigate the asymptotic behavior of the survival probability of a critical multitype branching process evolving in i.i.d. random environment. We show under rather general assumptions on the form of the…
A density-dependent branching process is a particle system in which individuals reproduce independently, but in a way that depends on the current population size. This feature can model a wide range of ecological interactions at the cost of…
Metastasis, the spread of cancer cells from a primary tumor to secondary location(s) in the human organism, is the ultimate cause of death for the majority of cancer patients. That is why, it is crucial to understand metastases evolution in…
In this work we model the dynamics of a population that evolves as a continuous time branching process with a trait structure and ecological interactions in form of mutations and competition between individuals. We generalize existing…
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 consider a supercritical Galton-Watson branching process with immigration. It is well known that under suitable conditions on the offspring and immigration distributions, there is a finite, strictly positive limit ${\mathcal{W}}$ for the…
We consider the critical branching processes in correlated random environment which is positively associated and study the probability of survival up to the n-th generation. Moreover, when the environment is given by fractional Brownian…