Results of Taylor and Marcus and Rosen on the total variation of Gaussian processes and local times of associated symmetric stable processes are extended to a large class of symmetric Lévy processes. In this extension, the increments variance σ2(h) of the Gaussian process is generalized to a regularly varying function with index 0 < α < 2. The total variation function ϕ(·) is generalized to [special characters omitted] where [special characters omitted] where 0 < α < 1, limh →0β(h) = 1 and limu →0 ε(u) = 0.
|Advisor:||Marcus, Michael B.|
|Commitee:||Rosen, Jay, Verzani, John|
|School:||City University of New York|
|School Location:||United States -- New York|
|Source:||DAI-B 70/04, Dissertation Abstracts International|
|Keywords:||Gaussian processes, Levy processes, Local times|
Copyright in each Dissertation and Thesis is retained by the author. All Rights Reserved
The supplemental file or files you are about to download were provided to ProQuest by the author as part of a
dissertation or thesis. The supplemental files are provided "AS IS" without warranty. ProQuest is not responsible for the
content, format or impact on the supplemental file(s) on our system. in some cases, the file type may be unknown or
may be a .exe file. We recommend caution as you open such files.
Copyright of the original materials contained in the supplemental file is retained by the author and your access to the
supplemental files is subject to the ProQuest Terms and Conditions of use.
Depending on the size of the file(s) you are downloading, the system may take some time to download them. Please be