{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/19184"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/19184","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Strong convergence to diffusion processes with application to queueing theory","abstract":"We show the almost sure uniform pathwise convergence of birth and death processes and random walks to Brownian motion with drift and sticky Brownian motion. We thus provide constructive definitions of such diffusions. 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In the first case we give a queueing application and in the latter case we provide the transition distribution of the sticky Brownian motion along with its local variations at zero and a law of the iterated logarithm.","abstract_has_math":false,"creators":["Amir, Abdelmadjid"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["Philipp, Walter"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2011,"date_issued":"2011-05-07T11:59:30Z","date_published":"2011-05-07T11:59:30Z","updated_at":"2026-07-22T22:25:12Z","subjects":["Mathematics","Statistics"],"languages":["eng"],"rights":["Copyright 1990 Amir, Abdelmadjid"],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["AAI9114161","(UMI)AAI9114161"],"render_values":[{"text":"AAI9114161","href":null,"code":true},{"text":"(UMI)AAI9114161","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/2142/19184","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Philipp, Walter"]},{"key":"dc:creator","label":"Author","values":["Amir, Abdelmadjid"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2011-05-07T11:59:30Z","10000-01-01","1990"]},{"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","Statistics"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["eng"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 1990 Amir, Abdelmadjid"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["AAI9114161","(UMI)AAI9114161","http://hdl.handle.net/2142/19184"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["We show the almost sure uniform pathwise convergence of birth and death processes and random walks to Brownian motion with drift and sticky Brownian motion. 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