{"id":{"repo_id":"ku","oai_identifier":"oai:kuscholarworks.ku.edu:1808/37541"},"canonical_url":"https://search.dev.ndltd.org/etd/ku/oai:kuscholarworks.ku.edu:1808/37541","repository":{"repo_id":"ku","name":"University of Kansas","base_url":"https://kuscholarworks.ku.edu/server/oai/request"},"display":{"title":"On Self-Similar Gaussian Processes","abstract":"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.","abstract_html":"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&#x27;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 &lt; 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.","abstract_has_math":false,"creators":["Lei, Pedro"],"institution":"University of Kansas","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":["Nualart, David"],"committee_chairs":[],"committee_members":[],"year":2012,"date_issued":"2012-01-01","date_published":"2012-01-01","updated_at":"2026-07-24T02:46:29Z","subjects":["Mathematics","Statistics","fractional Brownian motion","hitting time","local time","Self-similar Gaussian process","Skorohod integral","Tanaka's formula"],"languages":["en"],"rights":["Copyright held by the author."],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier.other","label":"Dc Identifier Other","values":["http://dissertations.umi.com/ku:12470"],"render_values":[{"text":"http://dissertations.umi.com/ku:12470","href":"http://dissertations.umi.com/ku:12470","code":true}]}]},"links":{"outbound_url":"https://hdl.handle.net/1808/37541","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Nualart, David"]},{"key":"dc:creator","label":"Author","values":["Lei, Pedro"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2026-04-15T15:01:52Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2026-04-15T15:01:52Z"]},{"key":"dc:date.issued","label":"Date","values":["2012-01-01"]},{"key":"dc:publisher","label":"Institution","values":["University of Kansas"]},{"key":"dc:type","label":"Dc Type","values":["Dissertation"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Mathematics","Statistics","fractional Brownian motion","hitting time","local time","Self-similar Gaussian process","Skorohod integral","Tanaka's formula"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language.iso","label":"Language (ISO)","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright held by the author."]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.other","label":"Dc Identifier Other","values":["http://dissertations.umi.com/ku:12470"]},{"key":"dc:identifier.uri","label":"Identifier URI","values":["https://hdl.handle.net/1808/37541"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["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."]},{"key":"dc:title","label":"Title","values":["On Self-Similar Gaussian Processes"]}]}],"canonical_facts":{"dc:contributor.advisor":["Nualart, David"],"dc:creator":["Lei, Pedro"],"dc:date.accessioned":["2026-04-15T15:01:52Z"],"dc:date.available":["2026-04-15T15:01:52Z"],"dc:date.issued":["2012-01-01"],"dc:description.abstract":["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."],"dc:identifier.other":["http://dissertations.umi.com/ku:12470"],"dc:identifier.uri":["https://hdl.handle.net/1808/37541"],"dc:language.iso":["en"],"dc:publisher":["University of Kansas"],"dc:rights":["Copyright held by the author."],"dc:subject":["Mathematics","Statistics","fractional Brownian motion","hitting time","local time","Self-similar Gaussian process","Skorohod integral","Tanaka's formula"],"dc:title":["On Self-Similar Gaussian Processes"],"dc:type":["Dissertation"]},"updated_at":"2026-07-24T02:46:29Z"}