Related papers: Branching random walks with ageing
Under mild non-degeneracy assumptions on branching rates in each generation, we provide a criterion for almost-sure extinction of a multi-type branching process with time-dependent branching rates. We also provide a criterion for the total…
We study a generalized branching random walk where particles breed at a rate which depends on the number of neighboring particles. Under general assumptions on the breeding rates we prove the existence of a phase where the population…
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 study a model for the spread of an infectious disease which incorporates spatial and temporal effects. The model is a delayed multi-type branching process in which types represent geographic regions while infected individuals reproduce…
We consider branching random walks and contact processes on infinite, connected, locally finite graphs whose reproduction and infectivity rates across edges are inversely proportional to vertex degree. We show that when the ambient graph is…
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 study supercritical age-structured branching models starting from a single particle with a random lifetime, where the reproduction law depends on the remaining lifetime of the parent. The lifespan of an individual is decided at its birth…
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 branching-selection particle system on the real line, introduced by Brunet and Derrida. In this model the size of the population is fixed to a constant $N$. At each step individuals in the population reproduce independently,…
We consider a particular Branching Random Walk in Random Environment (BRWRE) on $\sN_0$ started with one particle at the origin. Particles reproduce according to an offspring distribution (which depends on the location) and move either one…
The work continues the author's many-year research in theory of maximal branching processes, which are obtained from classical branching processes by replacing the summation of descendant numbers with taking the maximum. One can say that in…
An individual-based model of stochastic branching is proposed and studied, in which point particles drift in $\bar{\mathds{R}}_{+}:=[0,+\infty)$ towards the origin (edge) with unit speed, where each of them splits into two particles that…
We study a model of growing population that competes for resources. At each time step, all existing particles reproduce and the offspring randomly move to neighboring sites. Then at any site with more than one offspring, the particles are…
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…
Consideration is given to the continuous-time supercritical branching random walk over a multidimensional lattice with a finite number of particle generation sources of the same intensity both with and without constraint on the variance of…
We are interested in the evolving genealogy of a birth and death process with trait structure and ecological interactions. Traits are hereditarily transmitted from a parent to its offspring unless a mutation occurs. The dynamics may depend…
The symbiotic branching model describes the dynamics of a spatial two-type population, where locally particles branch at a rate given by the frequency of the other type combined with nearest-neighbour migration. This model generalizes…
We consider the diffusion approximation of branching processes in random environment (BPREs). This diffusion approximation is similar to and mathematically more tractable than BPREs. We obtain the exact asymptotic behavior of the survival…
Consider a continuous-state branching population constructed as a flow of nested subordinators. Inverting the subordinators and reversing time give rise to a flow of coalescing Markov processes (with negative jumps) which correspond to the…
We consider a continuous-time branching random walk on a multidimensional lattice in a random branching medium. It is theoretically known that, in such branching random walks, large rare fluctuations of the medium may lead to anomalous…