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January 2016 Branching Brownian motion in a strip: Survival near criticality
S. C. Harris, M. Hesse, A. E. Kyprianou
Ann. Probab. 44(1): 235-275 (January 2016). DOI: 10.1214/14-AOP972


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 the interval shrinks to the critical value at which survival is no longer possible. We combine spine techniques and a backbone decomposition to obtain exact asymptotics for the near-critical survival probability. This allows us to deduce the existence of a quasi-stationary limit result for the process conditioned on survival which reveals that the backbone thins down to a spine as we approach criticality.

This paper is motivated by recent work on survival of near critical branching Brownian motion with absorption at the origin by Aïdékon and Harris [Near-critical survival probability of branching Brownian motion with an absorbing barrier (2010) Unpublished manuscript] as well as the work of Berestycki et al. [Ann. Probab. 41 (2013) 527–618; J. Stat. Phys. 143 (2011) 833–854].


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S. C. Harris. M. Hesse. A. E. Kyprianou. "Branching Brownian motion in a strip: Survival near criticality." Ann. Probab. 44 (1) 235 - 275, January 2016.


Received: 1 December 2012; Revised: 1 February 2014; Published: January 2016
First available in Project Euclid: 2 February 2016

zbMATH: 1342.60149
MathSciNet: MR3456337
Digital Object Identifier: 10.1214/14-AOP972

Primary: 60E10 , 60J80

Keywords: Additive martingales , backbone decomposition , Branching Brownian motion , large deviations , Multiplicative martingales

Rights: Copyright © 2016 Institute of Mathematical Statistics


Vol.44 • No. 1 • January 2016
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