On Self-Similar Gaussian Processes

The work in my dissertation consists of three main parts. In the first part we have shown a decomposition of the bifractional Brownian motion with parameters H,K into the sum of a fractional Brownian motion with Hurst parameter HK plus a stochastic process with absolutely continuous trajectories. Some applications of this decomposition are discussed. In the second part we establish a change-of-variable formula for a class of Gaussian processes with a covariance function satisfying minimal regularity and integrability conditions. The existence of the local time and a version of Tanaka's formula are derived. These results are applied to a general class of self-similar processes that includes the bifractional Brownian motion. On the other hand, we establish a comparison result on the Laplace transform of the hitting time for a fractional Brownian motion with Hurst parameter H < 1/2 . Finally, the third part deals with the p-variation of the self-similar Gaussian process. We show the convergence in L^2 of the realized variation for a general Gaussian self-similar process.

Grantor dc:publisher

University of Kansas

Year dc:date.issued

2012

Author dc:creator

• Lei, Pedro

Advisor dc:contributor.advisor

• Nualart, David

• Mathematics
• Statistics
• fractional Brownian motion
• hitting time
• local time
• Self-similar Gaussian process
• Skorohod integral
• Tanaka's formula

Statement dc:rights

• Copyright held by the author.

Language dc:language.iso

en

Dc Identifier Other

http://dissertations.umi.com/ku:12470

OAI identifier oai:identifier

oai:kuscholarworks.ku.edu:1808/37541