The First Time of a Brownian Motion from an Unbounded Convex Domain
| Author(s) | Li, Wenbo | |
| Date Accessioned | 2005-02-17T17:00:02Z | |
| Date Available | 2005-02-17T17:00:02Z | |
| Publication Date | 2002 | |
| Abstract | Consider the first exit time, ˝D of a (d + 1)-dimensional Brownian motion from an unbounded open domain D = (x; y) 2 R d+1 : y > f(x); x 2 R d starting at (x0; f(x0) + 1) 2 R d+1 for some x0 2 R d , where the function f(x) on R d is convex and f(x) ! 1 as the Euclidean norm j x j ! 1 . Very general estimates for the asymptotics of log P (˝D > t) are given by using Gaussian techniques. In particular, for f(x) = exp fj x j p g , p > 0, lim t !1 t | en |
| Sponsor | Supported in part by NSF Grant DMS-9972012. | en |
| Extent | 234768 bytes | |
| MIME type | application/pdf | |
| URL | http://udspace.udel.edu/handle/19716/336 | |
| Language | en_US | |
| Publisher | Department of Mathematical Sciences | en |
| Part of Series | Technical Report: 2002-12 | |
| Keywords | Brownian Motion | en |
| Keywords | Bessel process | en |
| Keywords | asymptotic tail distribution | en |
| Keywords | exit probabilities | en |
| Keywords | Slepian's inequality | en |
| dc.subject.classification | AMS: 60G40, 60J65 | |
| Title | The First Time of a Brownian Motion from an Unbounded Convex Domain | en |
| Type | Technical Report | en |