# 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…

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## References

SHOWING 1-10 OF 58 REFERENCES

### Branching Brownian motion with selection

- Mathematics
- 2012

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

- Mathematics
- 2013

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

- Mathematics
- 2012

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

- Mathematics
- 2016

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

- Mathematics
- 2007

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…

### Further probabilistic analysis of the Fisher–Kolmogorov–Petrovskii–Piscounov equation: one sided travelling-waves

- Mathematics
- 2006

### Critical branching Brownian motion with absorption: Particle configurations

- Mathematics
- 2012

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

- Mathematics
- 2007

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

- Mathematics
- 2007

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

- Mathematics
- 2012

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…