Related papers: Critical Multitype Branching Processes with Random…
Coalescence processes have received a lot of attention in the context of conditional branching processes with fixed population size and non-overlapping generations. Here we focus on similar problems in the context of the standard…
By decomposing the random walk path, we construct a multitype branching process with immigration in random environment for corresponding random walk with bounded jumps in random environment. Then we give two applications of the branching…
We consider a branching process with Poissonian immigration where individuals have inheritable types. At rate theta, new individuals singly enter the total population and start a new population which evolves like a supercritical,…
We investigate the long-time evolution of branching diffusion processes (starting with a finite number of particles) in inhomogeneous media. The qualitative behavior of the processes depends on the intensity of the branching. In the…
The aim of this paper is to study the fluctuations of a general class of supercritical branching Markov processes with non-local branching mechanisms. We show the existence of three regimes according to the size of the spectral gap…
In this work, we study asymptotics of the genealogy of Galton-Watson processes. Thus we consider a offspring distribution such that the rescaled Galton-Watson processes converges to a continuous state branching process (CSBP) with jumps.…
We give sufficient conditions on the initial, offspring and immigration distributions under which the distribution of a not necessarily stationary Galton--Watson process with immigration is regularly varying at any fixed time.
In this work, several convergence results are established for nearly critical self-excited systems in which event arrivals are described by multivariate marked Hawkes point processes. Under some mild high-frequency assumptions, the rescaled…
A branching process in a Markovian environment consists of an irreducible Markov chain on a set of "environments" together with an offspring distribution for each environment. At each time step the chain transitions to a new random…
The paper discusses a family of Markov processes that represent many particle systems, and their limiting behaviour when the number of particles go to infinity. The first part concerns model of biological systems: a model for sympatric…
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…
Let $(Z_n)$ be a supercritical branching process in a random environment $% \zeta$, and $W$ be the limit of the normalized population size $Z_n/\mathbb{E%}(Z_n|\zeta)$. We show necessary and sufficient conditions for the existence of…
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…
This paper is devoted the the study of the mean field limit for many-particle systems undergoing jump, drift or diffusion processes, as well as combinations of them. The main results are quantitative estimates on the decay of fluctuations…
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…
In branching process theory, linear-fractional distributions are commonly used to model individual reproduction, especially when the goal is to obtain more explicit formulas than those derived under general model assumptions. In this…
For multitype branching processes with immigration evolving in a random environment and producing a final product we find the tail distribution of the size of the final product accumulated in the system for a life period. Using this result…
We study supercritical branching processes under the influence of an i.i.d. emigration component. We provide conditions, under which the lifetime of the process is finite respectively has a finite expectation. A new version of the…
We consider the evolution of populations under the joint action of mutation and differential reproduction, or selection. The population is modelled as a finite-type Markov branching process in continuous time, and the associated…
We consider a subcritical Galton--Watson tree conditioned on having $n$ vertices with outdegree in a fixed set $\Omega$. Under mild regularity assumptions we prove various limits related to the maximal offspring of a vertex as $n$ tends to…