Branching brownian motion with absorption

Harry Kesten

Stochastic Processes and their Applications, 1978, vol. 7, issue 1, 9-47

Abstract: We consider a branching diffusion {Zt}t[greater-or-equal, slanted]0 in which particles move during their life time according to a Brownian motion with drift -[mu] and variance coefficient [sigma]2, and in which each particle which enters the negative half line is instantaneously removed from the population. If particles die with probability c dt+o(dt) in [t,t+dt] and if the mean number of offspring per particle is m>1, then Zt dies out w.p.l. if [mu][greater-or-equal, slanted][mu]0[reverse not equivalent]{2[sigma]2c(m-1)}1/2. If [mu] 0} is only exp{-const.T1/3+0(logT)2}, and conditionally on {ZT>0} there are with high probability much fewer particles alive at time T than E{ZTZT0}.

Date: 1978
References: Add references at CitEc
Citations: View citations in EconPapers (5)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/0304-4149(78)90035-2
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:7:y:1978:i:1:p:9-47

Ordering information: This journal article can be ordered from
http://http://www.elsevier.com/wps/find/supportfaq.cws_home/regional
https://shop.elsevie ... _01_ooc_1&version=01

Access Statistics for this article

Stochastic Processes and their Applications is currently edited by T. Mikosch

More articles in Stochastic Processes and their Applications from Elsevier
Bibliographic data for series maintained by Catherine Liu ().