{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/19372"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/19372","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Weak convergence and the prediction process","abstract":"We first consider convergence in law of measurable processes with a general parameter set and a state space. To this end, we need to investigate topological properties of the space of measurable functions which is the paths space of measurable processes. Also a characterization of compact sets in the space is derived and some functionals on the space are discussed.","abstract_html":"We first consider convergence in law of measurable processes with a general parameter set and a state space. To this end, we need to investigate topological properties of the space of measurable functions which is the paths space of measurable processes. Also a characterization of compact sets in the space is derived and some functionals on the space are discussed.","abstract_has_math":false,"creators":["Tsukahara, Hideatsu"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Statistics","degree_department":null,"school":null,"contributors":["Monrad, Ditlev"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2011,"date_issued":"2011-05-07T12:05:29Z","date_published":"2011-05-07T12:05:29Z","updated_at":"2026-07-22T22:25:12Z","subjects":["Mathematics","Statistics"],"languages":["eng"],"rights":["Copyright 1996 Tsukahara, Hideatsu"],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["9780591199499","AAI9712467","(UMI)AAI9712467"],"render_values":[{"text":"9780591199499","href":null,"code":true},{"text":"AAI9712467","href":null,"code":true},{"text":"(UMI)AAI9712467","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/2142/19372","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Monrad, Ditlev"]},{"key":"dc:creator","label":"Author","values":["Tsukahara, Hideatsu"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2011-05-07T12:05:29Z","10000-01-01","1996"]},{"key":"dc:type","label":"Dc Type","values":["text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Statistics"]},{"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 1996 Tsukahara, Hideatsu"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["9780591199499","AAI9712467","(UMI)AAI9712467","http://hdl.handle.net/2142/19372"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["We first consider convergence in law of measurable processes with a general parameter set and a state space. To this end, we need to investigate topological properties of the space of measurable functions which is the paths space of measurable processes. Also a characterization of compact sets in the space is derived and some functionals on the space are discussed.","We then proceed to prove some properties of probability measures on the space of measurable functions. After investigating conditions on function spaces which guarantee that weak convergence may be proved by establishing finite-dimensional convergence and tightness, we prove necessary and sufficient conditions for convergence in law of measurable processes. These results are then applied to convergence of the prediction process; a special case where the given process is Markov is studied in detail.","We also derive two results on the prediction process which is not in the field of weak convergence. One is on the asymptotic behavior of the prediction process under absolutely continuity, and the other is an example which shows that the prediction process may lost Markov property if one uses a larger filtration than the natural one.","Made available in DSpace on 2011-05-07T12:05:29Z (GMT). No. of bitstreams: 2 license.txt: 4922 bytes, checksum: 910b249b4beec47e7ab768910c8f966f (MD5) 9712467.pdf: 3279184 bytes, checksum: 4afc4bc587b75307f0b2c41740d97218 (MD5) Previous issue date: 1996","Item marked as restricted to the 'UIUC Users [automated]' Group (id=2) by Howard Ding (hding2@illinois.edu) on 2011-05-07T14:36:31Z Item is restricted indefinitely.","Restriction data tranferred 2014-07-01T11:14:44-05:00 Original Data Group with Access UIUC Users [automated] Release Date: none Reason: ETDs are only available to UIUC Users without author permission","ETDs are only available to UIUC Users without author permission","U of I Only"]},{"key":"dc:title","label":"Title","values":["Weak convergence and the prediction process"]}]}],"canonical_facts":{"dc:contributor":["Monrad, Ditlev"],"dc:creator":["Tsukahara, Hideatsu"],"dc:date":["2011-05-07T12:05:29Z","10000-01-01","1996"],"dc:description":["We first consider convergence in law of measurable processes with a general parameter set and a state space. To this end, we need to investigate topological properties of the space of measurable functions which is the paths space of measurable processes. Also a characterization of compact sets in the space is derived and some functionals on the space are discussed.","We then proceed to prove some properties of probability measures on the space of measurable functions. After investigating conditions on function spaces which guarantee that weak convergence may be proved by establishing finite-dimensional convergence and tightness, we prove necessary and sufficient conditions for convergence in law of measurable processes. These results are then applied to convergence of the prediction process; a special case where the given process is Markov is studied in detail.","We also derive two results on the prediction process which is not in the field of weak convergence. One is on the asymptotic behavior of the prediction process under absolutely continuity, and the other is an example which shows that the prediction process may lost Markov property if one uses a larger filtration than the natural one.","Made available in DSpace on 2011-05-07T12:05:29Z (GMT). No. of bitstreams: 2 license.txt: 4922 bytes, checksum: 910b249b4beec47e7ab768910c8f966f (MD5) 9712467.pdf: 3279184 bytes, checksum: 4afc4bc587b75307f0b2c41740d97218 (MD5) Previous issue date: 1996","Item marked as restricted to the 'UIUC Users [automated]' Group (id=2) by Howard Ding (hding2@illinois.edu) on 2011-05-07T14:36:31Z Item is restricted indefinitely.","Restriction data tranferred 2014-07-01T11:14:44-05:00 Original Data Group with Access UIUC Users [automated] Release Date: none Reason: ETDs are only available to UIUC Users without author permission","ETDs are only available to UIUC Users without author permission","U of I Only"],"dc:identifier":["9780591199499","AAI9712467","(UMI)AAI9712467","http://hdl.handle.net/2142/19372"],"dc:language":["eng"],"dc:rights":["Copyright 1996 Tsukahara, Hideatsu"],"dc:subject":["Mathematics","Statistics"],"dc:title":["Weak convergence and the prediction process"],"dc:type":["text"],"thesis:degree_discipline":["Statistics"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Ph.D."],"thesis:institution_name":["University of Illinois at Urbana-Champaign"]},"updated_at":"2026-07-22T22:25:12Z"}