{"id":{"repo_id":"lsu-thes","oai_identifier":"oai:repository.lsu.edu:gradschool_dissertations-2066"},"canonical_url":"https://search.dev.ndltd.org/etd/lsu-thes/oai:repository.lsu.edu:gradschool_dissertations-2066","repository":{"repo_id":"lsu-thes","name":"Lousiana State University","base_url":"https://repository.lsu.edu/do/oai/"},"display":{"title":"The new stochastic integral and anticipating stochastic differential equations","abstract":"In this work, we develop further the theory of stochastic integration of adapted and instantly independent stochastic processes started by Wided Ayed and Hui-Hsiung Kuo in [1,2]. We provide a first counterpart to the It&ocirc isometry that accounts for both adapted and instantly independent processes. We also present several It&ocirc formulas for the new stochastic integral. Finally, we apply the new It&ocirc formula to solve a linear stochastic differential equations with anticipating initial conditions.","abstract_html":"In this work, we develop further the theory of stochastic integration of adapted and instantly independent stochastic processes started by Wided Ayed and Hui-Hsiung Kuo in [1,2]. We provide a first counterpart to the It&ocirc isometry that accounts for both adapted and instantly independent processes. We also present several It&ocirc formulas for the new stochastic integral. Finally, we apply the new It&ocirc formula to solve a linear stochastic differential equations with anticipating initial conditions.","abstract_has_math":false,"creators":["Szozda, Benedykt"],"institution":"Mathematics","degree_name":"Doctor of Philosophy (PhD)","degree_level":"Dissertation","degree_discipline":"Applied Mathematics","degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2012,"date_issued":"2012-01-01T08:00:00Z","date_published":"2012-01-01T08:00:00Z","updated_at":"2026-07-24T02:58:50Z","subjects":["stochastic integration","stochastic differential equations","Ito formula","Ito integral","anticipating stochastic integral","instantaneous independence","Brownian motion","instantly independent processes"],"languages":[],"rights":["unrestricted","Release the entire work immediately for access worldwide."],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["etd-06052012-150153","https://repository.lsu.edu/gradschool_dissertations/1067"],"render_values":[{"text":"etd-06052012-150153","href":null,"code":true},{"text":"https://repository.lsu.edu/gradschool_dissertations/1067","href":"https://repository.lsu.edu/gradschool_dissertations/1067","code":true}]}]},"links":{"outbound_url":"https://doi.org/10.31390/gradschool_dissertations.1067","outbound_label":"DOI","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Szozda, Benedykt"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2012-03-26"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2022-05-12T23:10:54Z"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Applied Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Doctor of Philosophy (PhD)"]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["Mathematics"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["stochastic integration","stochastic differential equations","Ito formula","Ito integral","anticipating stochastic integral","instantaneous independence","Brownian motion","instantly independent processes"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:rights","label":"Dc Rights","values":["unrestricted","Release the entire work immediately for access worldwide."]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["etd-06052012-150153","10.31390/gradschool_dissertations.1067","https://repository.lsu.edu/gradschool_dissertations/1067"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["In this work, we develop further the theory of stochastic integration of adapted and instantly independent stochastic processes started by Wided Ayed and Hui-Hsiung Kuo in [1,2]. We provide a first counterpart to the It&ocirc isometry that accounts for both adapted and instantly independent processes. We also present several It&ocirc formulas for the new stochastic integral. Finally, we apply the new It&ocirc formula to solve a linear stochastic differential equations with anticipating initial conditions."]},{"key":"dc:title","label":"Title","values":["The new stochastic integral and anticipating stochastic differential equations"]}]}],"canonical_facts":{"dc:creator":["Szozda, Benedykt"],"dc:date":["2012-03-26"],"dc:date.available":["2022-05-12T23:10:54Z"],"dc:description.abstract":["In this work, we develop further the theory of stochastic integration of adapted and instantly independent stochastic processes started by Wided Ayed and Hui-Hsiung Kuo in [1,2]. We provide a first counterpart to the It&ocirc isometry that accounts for both adapted and instantly independent processes. We also present several It&ocirc formulas for the new stochastic integral. Finally, we apply the new It&ocirc formula to solve a linear stochastic differential equations with anticipating initial conditions."],"dc:identifier":["etd-06052012-150153","10.31390/gradschool_dissertations.1067","https://repository.lsu.edu/gradschool_dissertations/1067"],"dc:rights":["unrestricted","Release the entire work immediately for access worldwide."],"dc:subject":["stochastic integration","stochastic differential equations","Ito formula","Ito integral","anticipating stochastic integral","instantaneous independence","Brownian motion","instantly independent processes"],"dc:title":["The new stochastic integral and anticipating stochastic differential equations"],"thesis:degree_discipline":["Applied Mathematics"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Doctor of Philosophy (PhD)"],"thesis:institution_name":["Mathematics"]},"updated_at":"2026-07-24T02:58:50Z"}