Related papers: Inverting the operation of conditioning a branchin…
We use a classical combinatorial inequality to establish a Markov inequality for multivariate binary Markov processes on trees. We then apply this result, alongside with the FKG inequality, to compare the expected loss of biodiversity under…
Branching processes are classical growth models in cell kinetics. In their construction, it is usually assumed that cell lifetimes are independent random variables, which has been proved false in experiments. Models of dependent lifetimes…
In this paper, we study the phenomenon of coming down from infinity for subcritical cooperative branching processes with pairwise interactions (BPI processes) under suitable conditions. BPI processes are continuous-time Markov chains that…
We extend earlier results on conditioning of super-Brownian motion to general branching rules. We obtain representations of the conditioned process, both as an $h$-transform, and as an unconditioned superprocess with immigration along a…
We consider the question of exponential decay to equilibrium of solutions of an abstract class of degenerate evolution equations on a Hilbert space modeling the steady Boltzmann and other kinetic equations. Specifically, we provide…
The paper has four goals. First, we want to generalize the classical concept of the branching property so that it becomes applicable for historical and genealogical processes (using the coding of genealogies by ($V$-marked) ultrametric…
In this paper we study a 2-type linear-fractional branching process in varying environment with asymptotically constant mean matrices. Let $\nu$ be the extinction time and for $k\ge1$ let $M_k$ be the mean matrix of offspring distribution…
In this paper we solve the inverse problem for a class of mean field models (Curie-Weiss model and its multi-species version) when multiple thermodynamic states are present, as in the low temperature phase where the phase space is…
We establish central limit theorems for a large class of supercritical branching Markov processes in infinite dimension with spatially dependent and non-necessarily local branching mechanisms. This result relies on a fourth moment…
Random-cluster measures on infinite regular trees are studied in conjunction with a general type of `boundary condition', namely an equivalence relation on the set of infinite paths of the tree. The uniqueness and non-uniqueness of…
In order to model random density-dependence in population dynamics, we construct the random analogue of the well-known logistic process in the branching process' framework. This density-dependence corresponds to intraspecific competition…
We study time continuous branching processes with exponentially distributed lifetimes, with two types of cells that proliferate according to binary fission. A range of possible system dynamics are considered, each of which is characterized…
Given a branching random walk on a graph, we consider two kinds of truncations: by inhibiting the reproduction outside a subset of vertices and by allowing at most $m$ particles per site. We investigate the convergence of weak and strong…
A multi-type branching process is defined as a random tree with labeled vertices, where each vertex produces offspring independently according to the same multivariate probability distribution. We demonstrate that in realizations of the…
This paper provides an adaptation of branching bisimilarity to reactive systems with time-outs that does not enable eliding of time-out transitions. Multiple equivalent definitions are procured, along with a modal characterisation and a…
Multitype branching processes are ideal for studying the population dynamics of stem cell populations undergoing mutation accumulation over the years following transplant. In such stochastic models, several quantities are of clinical…
Let $(Z_n)$ be a supercritical branching process in a random environment $\xi$. We study the convergence rates of the martingale $W_n = Z_n/ E[Z_n| \xi]$ to its limit $W$. The following results about the convergence almost sur (a.s.), in…
We consider one-dimensional branching Brownian motion in which particles are absorbed at the origin. We assume that when a particle branches, the offspring distribution is supercritical, but the particles are given a critical drift towards…
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.…
We consider subcritical branching processes with immigration which evolve under the influence of a random environment and study the tail distribution of life periods of such processes defined as the length of the time interval between the…