Quadratic Functionals and Small Ball Probabilities for the m-fold Brownian Motion
| Author(s) | Chen, X. | |
| Author(s) | Li, Wenbo | |
| Date Accessioned | 2005-02-17T17:09:25Z | |
| Date Available | 2005-02-17T17:09:25Z | |
| Publication Date | 2002 | |
| Abstract | Let the Gaussian process Xm(t) be the m-fold integrated Brownian motion for positive integer m. The Laplace transform of the quadratic functional of Xm(t) is found by using an appropriate self-adjoint integral operator. The result is then used to show the power of a general connection between small ball probabilities for Gaussian process. The connection is discovered by introducing an independent random shift. Various interplay between our results and principal eigenvalues for non-uniform elliptic generators on an unbounded domain are discussed. | en |
| Sponsor | Supported in part by NSF Grant DMS-0102238 and supported in part by NSF Grant DMS-9972012 | en |
| Extent | 278044 bytes | |
| MIME type | application/pdf | |
| URL | http://udspace.udel.edu/handle/19716/337 | |
| Language | en_US | |
| Publisher | Department of Mathematical Sciences | en |
| Part of Series | Technical Report: 2002-13 | |
| Keywords | The m-fold Integrated Brownian Motion | en |
| Keywords | quadratic functionals | en |
| Keywords | small ball probabilities | en |
| Keywords | principal eigenvalues | en |
| dc.subject.classification | AMS: 60G15, 60J25, 60J60 | |
| Title | Quadratic Functionals and Small Ball Probabilities for the m-fold Brownian Motion | en |
| Type | Technical Report | en |