Related papers: Conditioning the logistic continuous-state branchi…
Consider the continuous-time Markov Branching Process. In critical case we consider a situation when the generating function of intensity of transformation of particles has the infinite second moment, but its tail regularly varies in sense…
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…
In this paper we study the conditional limit theorems for critical continuous-state branching processes with branching mechanism $\psi(\lambda)=\lambda^{1+\alpha}L(1/\lambda)$ where $\alpha\in [0,1]$ and $L$ is slowly varying at $\infty$.…
For a branching process in random environment it is assumed that the offspring distribution of the individuals varies in a random fashion, independently from one generation to the other. Interestingly there is the possibility that the…
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…
Conditions for almost sure extinction are studied in discrete time branching processes with an infinite number of types. It is not assumed that the expected number of children is a bounded function of the parent's type. There might also be…
When the unconditioned process is a diffusion submitted to a space-dependent killing rate $k(\vec x)$, various conditioning constraints can be imposed for a finite time horizon $T$. We first analyze the conditioned process when one imposes…
We consider the diffusion approximation of branching processes in random environment (BPREs). This diffusion approximation is similar to and mathematically more tractable than BPREs. We obtain the exact asymptotic behavior of the survival…
In this paper, we consider time-inhomogeneous branching processes and time-inhomogeneous birth-and-death processes, in which the offspring distribution and birth and death rates (respectively) vary in time. A classical result of branching…
We investigate branching processes in nearly degenerate varying environment, where the offspring distribution converges to the degenerate distribution at 1. Such processes die out almost surely, therefore, we condition on non-extinction or…
For a branching process in random environment it is assumed that the offspring distribution of the individuals varies in a random fashion, independently from one generation to the other. For the subcritical regime a kind of phase transition…
We consider excursions for a class of stochastic processes describing a population of discrete individuals experiencing density-limited growth, such that the population has a finite carrying capacity and behaves qualitatively like the…
The spatial logistic branching process is a population dynamics model in which particles move on a lattice according to independent simple symmetric random walks, each particle splits into a random number of individuals at rate one, and…
We consider diffusion processes x_{t} on the unit interval. Doob-transformation techniques consist of a selection of x_{t}-paths procedure. The law of the transformed process is the one of a branching diffusion system of particles, each…
In this paper, we study the speed of extinction of continuous state branching processes in subcritical L\'evy environments. More precisely, when the associated L\'evy process to the environment drifts to $-\infty$ and, under a suitable…
We consider a stochastic logistic growth model involving both birth and death rates in the drift and diffusion coefficients for which extinction eventually occurs almost surely. The associated complete Fokker-Planck equation describing the…
We consider the setting of either a general non-local branching particle process or a general non-local superprocess. Under the assumption that the mean semigroup has a Perron-Frobenious type behaviour in combination with a regularly…
The subcritical Markov branching process X(t) starting with one particle as the initial condition has the ultimate extinction probability q = 1. The branching mechanism in consideration is defined by the mixture of logarithmic distributions…
We introduce a class of branching processes in which the reproduction or lifetime distribution at a given time depends on the total cumulative number of individuals who have been born in the population until that time. We focus on a…
When the unconditioned process is a diffusion living on the half-line $x \in ]-\infty,a[$ in the presence of an absorbing boundary condition at position $x=a$, we construct various conditioned processes corresponding to finite or infinite…