Related papers: Mixed state branching evolution for cell division …
We propose a new perspective on the asymptotic regimes of fast and slow extinction in the contact process on locally converging sequences of sparse finite graphs. We characterise the phase boundary by the existence of a metastable density,…
We consider the time evolution of the lattice subcritical Galton-Watson model with immigration. We prove Carleman type estimation for the cumulants in the simple case (binary splitting) and show the existence of a steady state. We also…
We study fluctuations of the empirical processes of a non-equilibrium interacting particle system consisting of two species over a domain that is recently introduced in [8] and establish its functional central limit theorem. This…
A Galton-Watson branching process with immigration evolving in a random environment is considered. Its associated random walk is assumed to be oscillating. We prove a functional limit theorem in which the process under consideration is…
Certain Markov processes, or deterministic evolution equations, have the property that they are dual to a stochastic process that exhibits extinction versus unbounded growth, i.e., the total mass in such a process either becomes zero, or…
The aim of this paper is to study the large population limit of a binary branching particle system with Moran type interactions: we introduce a new model where particles evolve, reproduce and die independently and, with a probability that…
We consider a class of multitype Galton-Watson branching processes with a countably infinite type set $\mathcal{X}_d$ whose mean progeny matrices have a block lower Hessenberg form. For these processes, the probability $\boldsymbol{q}(A)$…
We prove a general fluctuation limit theorem for Galton-Watson branching processes with immigration. The limit is a time-inhomogeneous OU type process driven by a spectrally positive Levy process. As applications of this result, we obtain…
In this paper we study a two-level branching model for virus populations under cell division. We assume that the cells are carrying virus populations which evolve as a branching particle system with competition, while the cells split…
A population genetics model based on a multitype branching process, or equivalently a Galton-Watson branching process for multiple alleles, is pre- sented. The diffusion limit forward Kolmogorov equation is derived for the case of neutral…
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.…
Conditioning a multitype Galton-Watson process to stay alive into the indefinite future leads to what is known as its associated $Q$-process. We show that the same holds true if the process is conditioned to reach a positive threshold or a…
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…
We consider the extinction events of Galton-Watson processes with countably infinitely many types. In particular, we construct truncated and augmented Galton-Watson processes with finite but increasing sets of types. A pathwise approach is…
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 investigate the temporal evolution and spatial propagation of branching annihilating random walks in one dimension. Depending on the branching and annihilation rates, a few-particle initial state can evolve to a propagating finite…
We observe the Galton-Watson Branching Processes. Limit properties of transition functions and their convergence to invariant measures are investigated.
We describe the evolution of the quantity of parasites in a population of cells which divide in continuous-time. The quantity of parasites in a cell follows a Feller diffusion, which is splitted randomly between the two daughter cells when…
We introduce multi-type Markov Branching trees, which are simple random population tree models where individuals are characterized by their size and type and give rise to (size,type)-children in a Galton-Watson fashion, with the rule that…
We consider a critical branching particle system in $\R^d$, composed of individuals of a finite number of types $i\in\{1,...,K\}$. Each individual of type $i$ moves independently according to a symmetric $\alpha_i$-stable motion. We assume…