Abstract
This paper is motivated by recent work on survival of near crit- ical branching Brownian motion with absorption at the origin by A ̈ıd ́ekon and Harris in [AH] as well as the work of Berestycki et al. in [BBS] and [BBS11].
| Language | English |
|---|---|
| Pages | 235-275 |
| Number of pages | 51 |
| Journal | Annals of Probability |
| Volume | 44 |
| Issue number | 1 |
| Early online date | 14 Jul 2015 |
| DOIs | |
| Status | Published - Jan 2016 |
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Keywords
- Branching Brownian motion
- backbone decomposition
- large deviations
- multiplicative martingales
- additive martingales
Cite this
Branching brownian motion in a strip : survival near criticality. / Harris, Simon; Hesse, Marion; Kyprianou, Andreas.
In: Annals of Probability, Vol. 44, No. 1, 01.2016, p. 235-275.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Branching brownian motion in a strip
T2 - Annals of Probability
AU - Harris, Simon
AU - Hesse, Marion
AU - Kyprianou, Andreas
PY - 2016/1
Y1 - 2016/1
N2 - 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 condi- tioned 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 crit- ical branching Brownian motion with absorption at the origin by A ̈ıd ́ekon and Harris in [AH] as well as the work of Berestycki et al. in [BBS] and [BBS11].
AB - 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 condi- tioned 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 crit- ical branching Brownian motion with absorption at the origin by A ̈ıd ́ekon and Harris in [AH] as well as the work of Berestycki et al. in [BBS] and [BBS11].
KW - Branching Brownian motion
KW - backbone decomposition
KW - large deviations
KW - multiplicative martingales
KW - additive martingales
UR - http://dx.doi.org/10.1214/14-AOP972
U2 - 10.1214/14-AOP972
DO - 10.1214/14-AOP972
M3 - Article
VL - 44
SP - 235
EP - 275
JO - Annals of Probability
JF - Annals of Probability
SN - 0091-1798
IS - 1
ER -