Open Access
Translator Disclaimer
2019 Non local branching Brownian motions with annihilation and free boundary problems
Anna De Masi, Pablo A. Ferrari, Errico Presutti, Nahuel Soprano-Loto
Electron. J. Probab. 24: 1-30 (2019). DOI: 10.1214/19-EJP324


We study a system of branching Brownian motions on $\mathbb{R} $ with annihilation: at each branching time a new particle is created and the leftmost one is deleted. The case of strictly local creations (the new particle is put exactly at the same position of the branching particle) was studied in [10]. In [11] instead the position $y$ of the new particle has a distribution $p(x,y)dy$, $x$ the position of the branching particle, however particles in between branching times do not move. In this paper we consider Brownian motions as in [10] and non local branching as in [11] and prove convergence in the continuum limit (when the number $N$ of particles diverges) to a limit density which satisfies a free boundary problem when this has classical solutions. We use in the convergence a stronger topology than in [10] and [11] and have explicit bounds on the rate of convergence.


Download Citation

Anna De Masi. Pablo A. Ferrari. Errico Presutti. Nahuel Soprano-Loto. "Non local branching Brownian motions with annihilation and free boundary problems." Electron. J. Probab. 24 1 - 30, 2019.


Received: 25 May 2018; Accepted: 21 May 2019; Published: 2019
First available in Project Euclid: 21 June 2019

zbMATH: 07089001
MathSciNet: MR3978213
Digital Object Identifier: 10.1214/19-EJP324

Primary: 60K35 , 82C20

Keywords: Branching Brownian motion , Brunet-Derrida models , free boundary problems , Hydrodynamic limit


Vol.24 • 2019
Back to Top