• Corpus ID: 235266111

# Branching Brownian motion in an expanding ball and application to the mild obstacle problem

@inproceedings{Oz2021BranchingBM,
title={Branching Brownian motion in an expanding ball and application to the mild obstacle problem},
author={Mehmet Oz},
year={2021}
}
We first consider a d-dimensional branching Brownian motion (BBM) evolving in an expanding ball, where the particles are killed at the boundary of the ball, and the expansion is subdiffusive in time. We study the large-time asymptotic behavior of the mass inside the ball, and obtain a large-deviation (LD) result as time tends to infinity on the probability that the mass is aytpically small. Then, we consider the problem of BBM among mild Poissonian obstacles, where a random ‘trap field’ in Rd…

## References

SHOWING 1-10 OF 23 REFERENCES

### Survival asymptotics for branching Brownian motion in a Poissonian trap field

• Mathematics
• 2001
In this paper we study a branching Brownian motion on Rd with branching rate in a Poissonian trap eld whose Borel intensity mea sure is such that d dx decays radially with the distance to the origin

### Optimal survival strategy for branching Brownian motion in a Poissonian trap field

• Mathematics
Annales de l'Institut Henri Poincaré, Probabilités et Statistiques
• 2019
We study a branching Brownian motion Z with a generic branching law, evolving in Rd, where a field of Poissonian traps is present. Each trap is a ball with constant radius. We focus on two cases of

### Conditional speed of branching Brownian motion, skeleton decomposition and application to random obstacles

• Mathematics
• 2015
We study a branching Brownian motion $Z$ in $\mathbb{R}^d$, among obstacles scattered according to a Poisson random measure with a radially decaying intensity. Obstacles are balls with constant

### Conditional speed of branching Brownian motion, skeleton decomposition and application to random obstacles

• Mathematics
• 2015
We study a branching Brownian motion $Z$ in $\mathbb{R}^d$, among obstacles scattered according to a Poisson random measure with a radially decaying intensity. Obstacles are balls with constant

### Branching Brownian motion in strip: survival near criticality

• Mathematics
• 2012
We consider a branching Brownian motion with linear drift in which particles are killed on exiting the interval (0,K) and study the evolution of the process on the event of survival as the width of

### Quenched law of large numbers for branching Brownian motion in a random medium

. We study a spatial branching model, where the underlying motion is d -dimensional ( d ≥ 1) Brownian motion and the branching rate is affected by a random collection of reproduction suppressing sets

### Survival of Near-Critical Branching Brownian Motion

• Mathematics
• 2011
Consider a system of particles performing branching Brownian motion with negative drift $\mu= \sqrt{2 - \varepsilon}$ and killed upon hitting zero. Initially there is one particle at x>0. Kesten