Boundary Non-crossings of Brownian Pillow
Details
Serval ID
serval:BIB_B88F8B062FDF
Type
Article: article from journal or magazin.
Collection
Publications
Institution
Title
Boundary Non-crossings of Brownian Pillow
Journal
Journal of Theoretical Probability
ISSN
0894-9840
1572-9230 ([electronic])
1572-9230 ([electronic])
Publication state
Published
Issued date
2010
Peer-reviewed
Oui
Volume
23
Number
1
Pages
193-208
Language
english
Abstract
Let B(0)(s, t) be a Brownian pillow with continuous sample paths, and let h, u : [0, 1](2) -> R be two measurable functions. In this paper we derive upper and lower bounds for the boundary non-crossing probability
psi (u; h) := P{B(0)(s, t) + h(s, t) <= u(s, t), for all s, t is an element of [0, 1]}.
Further we investigate the asymptotic behaviour of psi(u; gamma h) with gamma tending to infinity and solve a related minimisation problem.
psi (u; h) := P{B(0)(s, t) + h(s, t) <= u(s, t), for all s, t is an element of [0, 1]}.
Further we investigate the asymptotic behaviour of psi(u; gamma h) with gamma tending to infinity and solve a related minimisation problem.
Keywords
Boundary non-crossing probability, Brownian pillow with trend, Large deviations, Smallest concave majorant, Reproducing kernel Hilbert space, Small ball probabilities
Web of science
Create date
03/09/2010 9:56
Last modification date
20/08/2019 15:26
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