{"id":{"repo_id":"siu-theses","oai_identifier":"oai:opensiuc.lib.siu.edu:dissertations-1346"},"canonical_url":"https://search.dev.ndltd.org/etd/siu-theses/oai:opensiuc.lib.siu.edu:dissertations-1346","repository":{"repo_id":"siu-theses","name":"Southern Illinois University","base_url":"https://opensiuc.lib.siu.edu/do/oai/"},"display":{"title":"Closing the memory gap in stochastic functional differential equations","abstract":"In this paper, we obtain convergence of solutions of stochastic differential systems with memory gap to those with full finite memory. More specifically, solutions of stochastic differential systems with memory gap are processes in which the intrinsic dependence of the state on its history goes only up to a specific time in the past. As a consequence of this convergence, we obtain a new existence proof and approximation scheme for stochastic functional differential equations (SFDEs) whose coefficients have linear growth. In mathematical finance, an option pricing formula with full finite memory is obtained through convergence of stock dynamics with memory gap to stock dynamics with full finite memory.","abstract_html":"In this paper, we obtain convergence of solutions of stochastic differential systems with memory gap to those with full finite memory. More specifically, solutions of stochastic differential systems with memory gap are processes in which the intrinsic dependence of the state on its history goes only up to a specific time in the past. As a consequence of this convergence, we obtain a new existence proof and approximation scheme for stochastic functional differential equations (SFDEs) whose coefficients have linear growth. In mathematical finance, an option pricing formula with full finite memory is obtained through convergence of stock dynamics with memory gap to stock dynamics with full finite memory.","abstract_has_math":false,"creators":["Sancier-Barbosa, Flavia Cabral"],"institution":null,"degree_name":"Doctor of Philosophy","degree_level":"Campus Only Dissertation","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["Mohammed, Salah"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2011,"date_issued":"2011-05-01T07:00:00Z","date_published":"2011-05-01T07:00:00Z","updated_at":"2026-07-24T04:33:47Z","subjects":["approximation scheme","option pricing theory","stochastic functional differential equations"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://opensiuc.lib.siu.edu/dissertations/346","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Mohammed, Salah"]},{"key":"dc:creator","label":"Author","values":["Sancier-Barbosa, Flavia Cabral"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Campus Only Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Doctor of Philosophy"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["approximation scheme","option pricing theory","stochastic functional differential equations"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://opensiuc.lib.siu.edu/dissertations/346"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["In this paper, we obtain convergence of solutions of stochastic differential systems with memory gap to those with full finite memory. More specifically, solutions of stochastic differential systems with memory gap are processes in which the intrinsic dependence of the state on its history goes only up to a specific time in the past. As a consequence of this convergence, we obtain a new existence proof and approximation scheme for stochastic functional differential equations (SFDEs) whose coefficients have linear growth. In mathematical finance, an option pricing formula with full finite memory is obtained through convergence of stock dynamics with memory gap to stock dynamics with full finite memory."]},{"key":"dc:title","label":"Title","values":["Closing the memory gap in stochastic functional differential equations"]}]}],"canonical_facts":{"dc:contributor":["Mohammed, Salah"],"dc:creator":["Sancier-Barbosa, Flavia Cabral"],"dc:description.abstract":["In this paper, we obtain convergence of solutions of stochastic differential systems with memory gap to those with full finite memory. More specifically, solutions of stochastic differential systems with memory gap are processes in which the intrinsic dependence of the state on its history goes only up to a specific time in the past. As a consequence of this convergence, we obtain a new existence proof and approximation scheme for stochastic functional differential equations (SFDEs) whose coefficients have linear growth. In mathematical finance, an option pricing formula with full finite memory is obtained through convergence of stock dynamics with memory gap to stock dynamics with full finite memory."],"dc:identifier":["https://opensiuc.lib.siu.edu/dissertations/346"],"dc:subject":["approximation scheme","option pricing theory","stochastic functional differential equations"],"dc:title":["Closing the memory gap in stochastic functional differential equations"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_level":["Campus Only Dissertation"],"thesis:degree_name":["Doctor of Philosophy"]},"updated_at":"2026-07-24T04:33:47Z"}