Related papers: Local extinction in continuous-state branching pro…
In this paper, we review recent results of ours concerning branching processes with general lifetimes and neutral mutations, under the infinitely many alleles model, where mutations can occur either at birth of individuals or at a constant…
We establish the exponential ergodic property in a weighted total variation distance of continuous-state branching processes with immigration in random environments with competition and catastrophes, under a Lyapunov-type condition and…
We introduce a class of one-dimensional positive Markov processes generalizing continuous-state branching processes (CBs), by taking into account a phenomenon of random collisions. Besides branching, characterized by a general mechanism…
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 a birth and death process in which death is due to both `natural death' and to competition between individuals, modelled as a quadratic function of population size. The resulting `logistic branching process' has been proposed as…
We define the height process for super-critical continuous state branching processes with quadratic branching mechanism. It appears as a projective limit of Brownian motions with positive drift reflected at 0 and a>0 as a goes to infinity.…
Splitting trees are those random trees where individuals give birth at constant rate during a lifetime with general distribution, to i.i.d. copies of themselves. The width process of a splitting tree is then a binary, homogeneous…
This paper investigates the long-time behavior of double branching annihilating random walkers with nearest-neighbor dependent rates. The system consists of even number of particles which can execute nearest-neighbor random walk and they…
We establish general sufficient conditions for a sequence of controlled branching processes to converge weakly on the Skorokhod space. We focus on a class of controlled random variables that extends previous results by considering them as a…
In this paper, for $\alpha\in (1, 2}$ we show that the $\alpha$-stable continuous-state branching process and the associated process conditioned never to become extinct are positive self-similar Markov processes. Understanding the…
We study asymptotic behavior of conditional least squares estimators for 2-type doubly symmetric critical irreducible continuous state and continuous time branching processes with immigration based on discrete time (low frequency)…
We study age-structured branching models with reproduction law depending on the remaining lifetime of the parent. The lifespan of an individual is decided at its birth and its remaining lifetime decreases at the unit speed. The models…
We analyze the stationary tail of a fixed-point equation arising in branching processes with state-independent immigration, when both immigration and offspring distributions have heavy tails with boundary index one. We prove that \[ P(X >…
We propose a misanthrope process, defined on a ring, which realizes the totally asymmetric simple exclusion process with open boundaries. In the misanthrope process, particles have no exclusion interactions in contrast to those in the…
Our purpose is to estimate the posterior distribution of the parameters of interest for controlled branching processes (CBPs) without prior knowledge of the maximum number of offspring that an individual can give birth to and without…
This article studies the stability of solutions of equilibrium equations arising in so-called resource dependent branching processes. We argue that these new models, building on the model already presented by Bruss (1984 a), refined and…
It has been recently suggested that a totally asymmetric exclusion process with two species on an open chain could exhibit spontaneous symmetry breaking in some range of the parameters defining its dynamics. The symmetry breaking is…
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…
In this work, a variant of the birth and death chain with constant intensities, originally introduced by Bruno de Finetti way back in 1957, is revisited. This fact is also underlined by the choice of the title, which is clearly a literal…
We give conditions under which near-critical stochastic processes on the half-line have infinitely many or finitely many cutpoints, generalizing existing results on nearest-neighbour random walks to adapted processes with bounded increments…