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Survival probabilities for branching Brownian motion with absorption

Dublin Core		PKP Metadata Items	Metadata for this Document
1.	Title	Title of document	Survival probabilities for branching Brownian motion with absorption
2.	Creator	Author's name, affiliation, country	John William Harris; University of Bristol
2.	Creator	Author's name, affiliation, country	Simon C Harris; University of Bath
3.	Subject	Discipline(s)
3.	Subject	Keyword(s)	Branching Brownian motion with absorption; spine constructions; additive martingales.
3.	Subject	Subject classification	60J80
4.	Description	Abstract	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 origin. In the case $\rho>\sqrt{2\beta}$ the extinction time for this process, $\zeta$, is known to be finite almost surely. The main result of this article is a large-time asymptotic formula for the survival probability $P^x(\zeta>t)$ in the case $\rho>\sqrt{2\beta}$, where $P^x$ is the law of the BBM with absorption started from a single particle at the position $x>0$. We also introduce an additive martingale, $V$, for the BBM with absorption, and then ascertain the convergence properties of $V$. Finally, we use $V$ in a `spine' change of measure and interpret this in terms of `conditioning the BBM to survive forever' when $\rho>\sqrt{2\beta}$, in the sense that it is the large $t$-limit of the conditional probabilities $P^x(A\mid \zeta > t+s)$, for $A\in F_s$.
5.	Publisher	Organizing agency, location
6.	Contributor	Sponsor(s)	Engineering and Physical Sciences Research Council.
7.	Date	(YYYY-MM-DD)	2007-04-07
8.	Type	Status & genre	Peer-reviewed Article
8.	Type	Type
9.	Format	File format	PDF
10.	Identifier	Uniform Resource Identifier	http://ecp.ejpecp.org/article/view/1259
10.	Identifier	Digital Object Identifier	10.1214/ECP.v12-1259
11.	Source	Journal/conference title; vol., no. (year)	Electronic Communications in Probability; Vol 12
12.	Language	English=en
14.	Coverage	Geo-spatial location, chronological period, research sample (gender, age, etc.)
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