{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/71201"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/71201","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Limit Theorems for Weakly Dependent Random Vectors","abstract":"In Chapter I we improve upon results on the almost sure approximation of the empirical process of weakly dependent random vectors, recently obtained by Berkes and Philipp and Philipp and Pinzur. For strongly mixing sequences we relax the bounds on the mixing rates, and for absolutely regular sequences we improve the error term. We also extend these results to random vectors which are functions of the given sequence as well as to random variables which are evaluated at lacunary sequences.","abstract_html":"In Chapter I we improve upon results on the almost sure approximation of the empirical process of weakly dependent random vectors, recently obtained by Berkes and Philipp and Philipp and Pinzur. For strongly mixing sequences we relax the bounds on the mixing rates, and for absolutely regular sequences we improve the error term. We also extend these results to random vectors which are functions of the given sequence as well as to random variables which are evaluated at lacunary sequences.","abstract_has_math":false,"creators":["Dhompongsa, Sompong"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2014,"date_issued":"2014-12-16T06:18:02Z","date_published":"2014-12-16T06:18:02Z","updated_at":"2026-07-22T22:26:04Z","subjects":["Mathematics"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["(UMI)AAI8209564"],"render_values":[{"text":"(UMI)AAI8209564","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/2142/71201","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Dhompongsa, Sompong"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2014-12-16T06:18:02Z","10000-01-01","1982"]},{"key":"dc:type","label":"Dc Type","values":["text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph.D."]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Illinois at Urbana-Champaign"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Mathematics"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/71201","(UMI)AAI8209564"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["In Chapter I we improve upon results on the almost sure approximation of the empirical process of weakly dependent random vectors, recently obtained by Berkes and Philipp and Philipp and Pinzur. For strongly mixing sequences we relax the bounds on the mixing rates, and for absolutely regular sequences we improve the error term. We also extend these results to random vectors which are functions of the given sequence as well as to random variables which are evaluated at lacunary sequences.","In Chapter 2 we extend the uniform law of the iterated logarithm for classes of functions in Lip (alpha) ((alpha) > 1/2) evaluated at lacunary sequences and functions of mixing processes, due to Kaufman and Philipp. Here we relax the lacunarity condition and the mixing rates.","Made available in DSpace on 2014-12-16T06:18:02Z (GMT). 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For strongly mixing sequences we relax the bounds on the mixing rates, and for absolutely regular sequences we improve the error term. We also extend these results to random vectors which are functions of the given sequence as well as to random variables which are evaluated at lacunary sequences.","In Chapter 2 we extend the uniform law of the iterated logarithm for classes of functions in Lip (alpha) ((alpha) > 1/2) evaluated at lacunary sequences and functions of mixing processes, due to Kaufman and Philipp. Here we relax the lacunarity condition and the mixing rates.","Made available in DSpace on 2014-12-16T06:18:02Z (GMT). No. of bitstreams: 1 8209564.pdf: 2605218 bytes, checksum: 9ce19fa94cb5b0c6ed52ec4d2c4457c6 (MD5) Previous issue date: 1982","Embargo set by: Seth Robbins for item 71367 Lift date: Forever Reason: Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs","Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs","U of I Only","142 p.","Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1982."],"dc:identifier":["http://hdl.handle.net/2142/71201","(UMI)AAI8209564"],"dc:subject":["Mathematics"],"dc:title":["Limit Theorems for Weakly Dependent Random Vectors"],"dc:type":["text"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Ph.D."],"thesis:institution_name":["University of Illinois at Urbana-Champaign"]},"updated_at":"2026-07-22T22:26:04Z"}