Authors
Citation
P. Berthet et Z. Shi, Small ball estimates for Brownian motion under a weighted sup-norm, ST SCI M H, 36(1-2), 2000, pp. 275-289
Citations number
25
Categorie Soggetti
Mathematics
Journal title
STUDIA SCIENTIARUM MATHEMATICARUM HUNGARICA
ISSN journal
00816906
→ ACNP
Volume
36
Issue
1-2
Year of publication
2000
Pages
275 - 289
Database
ISI
SICI code
0081-6906(2000)36:1-2<275:SBEFBM>2.0.ZU;2-1
Abstract
Let {W(t); 0 less than or equal to t less than or equal to 1} be a real-val
ued Wiener process, starting from 0. For a large class of functions f which
may vanish at 0, rye obtain the exact asymptotics, as epsilon goes to 0, o
f log P(sup(0<t less than or equal to 1) \W(t)/f(t)\ <epsilon).