ATTENTION: The software behind KU ScholarWorks is being upgraded to a new version. Starting July 15th, users will not be able to log in to the system, add items, nor make any changes until the new version is in place at the end of July. Searching for articles and opening files will continue to work while the system is being updated.
If you have any questions, please contact Marianne Reed at mreed@ku.edu .
Limit distributions for functionals of Gaussian processes
dc.contributor.advisor | Nualart, David | |
dc.contributor.author | Jaramillo, Arturo | |
dc.date.accessioned | 2019-05-12T17:57:15Z | |
dc.date.available | 2019-05-12T17:57:15Z | |
dc.date.issued | 2018-05-31 | |
dc.date.submitted | 2018 | |
dc.identifier.other | http://dissertations.umi.com/ku:15911 | |
dc.identifier.uri | http://hdl.handle.net/1808/27886 | |
dc.description.abstract | This thesis is devoted to the study of the convergence in distribution of functionals of Gaussian processes. Most of the problems that we present are addressed by using an approach based on Malliavin calculus techniques. Our main contributions are the following: First, we study the asymptotic law of the approximate derivative of the self-intersection local time (SILT) in $[0,T]$ for the fractional Brownian motion. In order to do this, we describe the asymptotic behavior of the associated chaotic components and show that the first chaos approximates the SILT in $L^2$. Secondly, we examine the asymptotic law of the approximate self-intersection local time process for the fractional Brownian motion. We achieve this in two steps: the first part consists on proving the convergence of the finite dimensional distributions by using the `multidimensional fourth moment theorem'. The second part consists on proving the tightness property, for which we follow an approach based on Malliavin calculus techniques. The third problem consists on proving a non-central limit theorem for the process of weak symmetric Riemann sums for a wide variety of self-similar Gaussian processes. We address this problem by using the so-called small blocks-big blocks methodology and a central limit theorem for the power variations of self-similar Gaussian processes. Finally, we address the problem of determining conditions under which the eigenvalues of an Hermitian matrix-valued Gaussian process collide with positive probability. | |
dc.format.extent | 259 pages | |
dc.language.iso | en | |
dc.publisher | University of Kansas | |
dc.rights | Copyright held by the author. | |
dc.subject | Mathematics | |
dc.subject | Statistics | |
dc.subject | Theoretical mathematics | |
dc.subject | fracional Brownian motion | |
dc.subject | limit theorems | |
dc.subject | Local times | |
dc.subject | Malliavin calculus | |
dc.subject | random matrices | |
dc.subject | stochastic integration | |
dc.title | Limit distributions for functionals of Gaussian processes | |
dc.type | Dissertation | |
dc.contributor.cmtemember | Feng, Jin | |
dc.contributor.cmtemember | Liu, Zhipeng | |
dc.contributor.cmtemember | Soo, Terry | |
dc.contributor.cmtemember | Zhang, Jianbo | |
dc.thesis.degreeDiscipline | Mathematics | |
dc.thesis.degreeLevel | Ph.D. | |
dc.identifier.orcid | https://orcid.org/0000-0002-7650-4235 | |
dc.rights.accessrights | openAccess |
Files in this item
This item appears in the following Collection(s)
-
Dissertations [4889]
-
Mathematics Dissertations and Theses [179]