Citation
Wv. Li et Qm. Shao, Capture time of Brownian pursuits, PROB TH REL, 121(1), 2001, pp. 30-48
Citations number
19
Categorie Soggetti
Mathematics
Journal title
PROBABILITY THEORY AND RELATED FIELDS
ISSN journal
01788051
→ ACNP
Volume
121
Issue
1
Year of publication
2001
Pages
30 - 48
Database
ISI
SICI code
0178-8051(200109)121:1<30:CTOBP>2.0.ZU;2-R
Abstract
Let B-0, B-1, ... , B-n be independent standard Brownian motions, starting
at 0. We investigate the tail of the capture time
tau (n), = inf {t > 0 : B-i (t) - b(i) = B-0 (t) for some 1 less than or eq
ual to i less than or equal to n}
where 0 < b(i) less than or equal to 1, 1 < i less than or equal to n. In p
articular, we have E tau (3) = infinity and E tau (5) < infinity. Various g
eneralizations are also studied.