Related papers: Branching Processes -- A General Concept
We consider the long-term behaviour of critical multitype branching processes conditioned on non-extinction, both with respect to the forward and the ancestral processes. Forward in time, we prove a functional limit theorem in the space of…
We introduce a growth process which samples sections of uniform infinite causal triangulations by elementary moves in which a single triangle is added. A relation to a random walk on the integer half line is shown. This relation is used to…
We study the branching random walk on weighted graphs; site-breeding and edge-breeding branching random walks on graphs are seen as particular cases. We describe the strong critical value in terms of a geometrical parameter of the graph. We…
Suppose that $X=(X_{t})_{t\ge 0}$ is either a general supercritical non-local branching Markov process, or a general supercritical non-local superprocess, on a Luzin space. Here, by ``supercritical" we mean that the mean semigroup of $X$…
We introduce and study a class of probabilistic generative models, where the latent object is a finite-dimensional diffusion process on a finite time interval and the observed variable is drawn conditionally on the terminal point of the…
Given suitable functions $V, \Psi:[0,\infty) \to [0,\infty)$, we obtain necessary and sufficient conditions on $V,\Psi$ for the existence of a metric measure space and a symmetric diffusion process that satisfies sub-Gaussian heat kernel…
We define a multi-type coalescent point process of a general branching process with finitely many types. This multi-type coalescent fully describes the genealogy of the (quasi-stationary) standing population, providing types along ancestral…
We study the large deviation behaviour of the trajectories of empirical distributions of independent copies of time-homogeneous Feller processes on locally compact metric spaces. Under the condition that we can find a suitable core for the…
We present two iterative methods for computing the global and partial extinction probability vectors for Galton-Watson processes with countably infinitely many types. The probabilistic interpretation of these methods involves truncated…
Consider the mutually catalytic branching process with finite branching rate $\gamma$. We show that as $\gamma\to\infty$, this process converges in finite-dimensional distributions (in time) to a certain discontinuous process. We give…
We consider a discrete-time host-parasite model for a population of cells which are colonized by proliferating parasites. The cell population grows like an ordinary Galton-Watson process, but in reflection of real biological settings the…
We derive some additional results on the Bienyam\'e-Galton-Watson branching process with $\theta -$linear fractional branching mechanism, as studied in \cite{Sag}. This includes: the explicit expression of the limit laws in both the…
We consider an exactly solvable model of branching random walk with random selection, which describes the evolution of a population with $N$ individuals on the real line. At each time step, every individual reproduces independently, and its…
A general continuous-state branching processes in random environment (CBRE-process) is defined as the strong solution of a stochastic integral equation. The environment is determined by a L\'evy process with no jump less than $-1$. We give…
It is well known that the mean field theory of directed polymers in a random medium exhibits replica symmetry breaking with a distribution of overlaps which consists of two delta functions. Here we show that the leading finite size…
Linear fractional Galton-Watson branching processes in i.i.d.~random environment are, on the quenched level, intimately connected to random difference equations by the evolution of the random parameters of their linear fractional marginals.…
We consider the exploration process associated to the continuous random tree (CRT) built using a Levy process with no negative jumps. This process has been studied by Duquesne, Le Gall and Le Jan. This measure-valued Markov process is a…
A phylogenetic tree shows the evolutionary relationships among species. Internal nodes of the tree represent speciation events and leaf nodes correspond to species. A goal of phylogenetics is to combine such trees into larger trees, called…
We provide sufficient conditions for polynomial rate of convergence in the weak law of large numbers for supercritical general indecomposable multi-type branching processes. The main result is derived by investigating the embedded…
In this work, we introduce a spatial branching process to model the growth of the mycelial network of a filamentous fungus. In this model, each filament is described by the position of its tip, the trajectory of which is solution to a…