Yaglom-type limit theorems for branching Brownian motion with absorption

@article{Maillard2020YaglomtypeLT,
  title={Yaglom-type limit theorems for branching Brownian motion with absorption},
  author={Pascal Maillard and Jason Schweinsberg},
  journal={Annales Henri Lebesgue},
  year={2020}
}
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 origin so that the process eventually goes extinct with probability one. We establish precise asymptotics for the probability that the process survives for a large time t, building on previous results by Kesten (1978) and Berestycki, Berestycki, and… 

A branching particle system as a model of semi pushed fronts

We consider a system of particles performing a one-dimensional dyadic branching Brownian motion with space-dependent branching rate, negative drift −μ and killed upon reaching 0, starting with N

Branching Brownian Motion with Self-Repulsion

We consider a model of branching Brownian motion with self-repulsion. Self-repulsion is introduced via a change of measure that penalises particles spending time in an $$\epsilon $$ ϵ

Maximum of Branching Brownian Motion among mild obstacles

. We study the height of the maximal particle at time t of a one dimensional branching Brownian motion with a space-dependent branching rate. The branching rate is set to zero in finitely many

A Gaussian particle distribution for branching Brownian motion with an inhomogeneous branching rate

Motivated by the goal of understanding the evolution of populations undergoing selection, we consider branching Brownian motion in which particles independently move according to one-dimensional

References

SHOWING 1-10 OF 58 REFERENCES

Branching Brownian motion with selection

In this thesis, branching Brownian motion (BBM) is a random particle system where the particles diffuse on the real line according to Brownian motions and branch at constant rate into a random number

The genealogy of branching Brownian motion with absorption

We consider a system of particles which perform branching Brownian motion with negative drift and are killed upon reaching zero, in the near-critical regime where the total population stays roughly

Critical branching Brownian motion with absorption: survival probability

We consider branching Brownian motion on the real line with absorption at zero, in which particles move according to independent Brownian motions with the critical drift of $$-\sqrt{2}$$-2. Kesten

Speed and fluctuations of N-particle branching Brownian motion with spatial selection

We consider branching Brownian motion on the real line with the following selection mechanism: every time the number of particles exceeds a (large) given number N, only the N right-most particles are

Survival probabilities for branching Brownian motion with absorption

We study a branching Brownian motion (BBM) with absorption, in which particles move as Brownian motions with drift $-\rho$, undergo dyadic branching at rate $\beta>0$, and are killed on hitting the

Critical branching Brownian motion with absorption: Particle configurations

We consider critical branching Brownian motion with absorption, in which there is initially a single particle at x > 0, particles move according to independent one-dimensional Brownian motions with

Quasi-stationary distributions and diffusion models in population dynamics

In this paper, we study quasi-stationarity for a large class of Kolmogorov diffusions. The main novelty here is that we allow the drift to go to $- \infty$ at the origin, and the diffusion to have an

The survival probability of a branching random walk in presence of an absorbing wall

A branching random walk in presence of an absorbing wall moving at a constant velocity v undergoes a phase transition as v varies. The problem can be analyzed using the properties of the

Quasi-stationary distributions and population processes

This survey concerns the study of quasi-stationary distributions with a specific focus on models derived from ecology and population dynamics. We are concerned with the long time behavior of
...