{"id":{"repo_id":"passau-thes","oai_identifier":"oai:kobv.de-opus4-uni-passau:810"},"canonical_url":"https://search.dev.ndltd.org/etd/passau-thes/oai:kobv.de-opus4-uni-passau:810","repository":{"repo_id":"passau-thes","name":"Universität Passau","base_url":"https://opus4.kobv.de/opus4-uni-passau/oai"},"display":{"title":"Strongly Asymptotically Optimal Methods for the Pathwise Global Approximation of Stochastic Differential Equations with Coefficients of Super-linear Growth","abstract":"Our subject of study is strong approximation of stochastic differential equations (SDEs) with respect to the supremum and the L_p error criteria, and we seek approximations that are strongly asymptotically optimal in specific classes of approximations. For the supremum error, we prove strong asymptotic optimality for specific tamed Euler schemes relating to certain adaptive and to equidistant time discretizations. For the L_p error, we prove strong asymptotic optimality for specific tamed Milstein schemes relating to certain adaptive and to equidistant time discretizations. To illustrate our findings, we numerically analyze the SDE associated with the Heston–3/2–model originating from mathematical finance.","abstract_html":"Our subject of study is strong approximation of stochastic differential equations (SDEs) with respect to the supremum and the L_p error criteria, and we seek approximations that are strongly asymptotically optimal in specific classes of approximations. For the supremum error, we prove strong asymptotic optimality for specific tamed Euler schemes relating to certain adaptive and to equidistant time discretizations. For the L_p error, we prove strong asymptotic optimality for specific tamed Milstein schemes relating to certain adaptive and to equidistant time discretizations. To illustrate our findings, we numerically analyze the SDE associated with the Heston–3/2–model originating from mathematical finance.","abstract_has_math":false,"creators":["Hatzesberger, Simon"],"institution":"Universität Passau","degree_name":null,"degree_level":"thesis.doctoral","degree_discipline":null,"degree_department":null,"school":null,"contributors":["Müller-Gronbach, Thomas","Sabanis, Sotirios"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2020,"date_issued":"2020-02-21","date_published":"2020-02-21","updated_at":"2026-07-24T03:45:06Z","subjects":["Stochastic differential equation","Strong approximation","Strong asymptotic optimality","Asymptotic lower error bounds","Asymptotic upper error bounds"],"languages":[],"rights":["Creative Commons - CC BY-SA - Namensnennung - Weitergabe unter gleichen Bedingungen 4.0 International"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://opus4.kobv.de/opus4-uni-passau/frontdoor/index/index/docId/810","outbound_label":"Repository record","outbound_source":"source_url"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Müller-Gronbach, Thomas","Sabanis, Sotirios"]},{"key":"dc:creator","label":"Author","values":["Hatzesberger, Simon"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:publisher","label":"Institution","values":["Universität Passau"]},{"key":"dc:type","label":"Dc Type","values":["doctoralThesis"]},{"key":"thesis:degree_level","label":"Degree Level","values":["thesis.doctoral"]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["Universität Passau"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Stochastic differential equation","Strong approximation","Strong asymptotic optimality","Asymptotic lower error bounds","Asymptotic upper error bounds"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:rights","label":"Dc Rights","values":["Creative Commons - CC BY-SA - Namensnennung - Weitergabe unter gleichen Bedingungen 4.0 International"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["Our subject of study is strong approximation of stochastic differential equations (SDEs) with respect to the supremum and the L_p error criteria, and we seek approximations that are strongly asymptotically optimal in specific classes of approximations. For the supremum error, we prove strong asymptotic optimality for specific tamed Euler schemes relating to certain adaptive and to equidistant time discretizations. For the L_p error, we prove strong asymptotic optimality for specific tamed Milstein schemes relating to certain adaptive and to equidistant time discretizations. To illustrate our findings, we numerically analyze the SDE associated with the Heston–3/2–model originating from mathematical finance."]},{"key":"dc:format.medium","label":"Dc Format Medium","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Strongly Asymptotically Optimal Methods for the Pathwise Global Approximation of Stochastic Differential Equations with Coefficients of Super-linear Growth"]}]}],"canonical_facts":{"dc:contributor":["Müller-Gronbach, Thomas","Sabanis, Sotirios"],"dc:creator":["Hatzesberger, Simon"],"dc:description.abstract":["Our subject of study is strong approximation of stochastic differential equations (SDEs) with respect to the supremum and the L_p error criteria, and we seek approximations that are strongly asymptotically optimal in specific classes of approximations. For the supremum error, we prove strong asymptotic optimality for specific tamed Euler schemes relating to certain adaptive and to equidistant time discretizations. For the L_p error, we prove strong asymptotic optimality for specific tamed Milstein schemes relating to certain adaptive and to equidistant time discretizations. To illustrate our findings, we numerically analyze the SDE associated with the Heston–3/2–model originating from mathematical finance."],"dc:format.medium":["application/pdf"],"dc:publisher":["Universität Passau"],"dc:rights":["Creative Commons - CC BY-SA - Namensnennung - Weitergabe unter gleichen Bedingungen 4.0 International"],"dc:subject":["Stochastic differential equation","Strong approximation","Strong asymptotic optimality","Asymptotic lower error bounds","Asymptotic upper error bounds"],"dc:title":["Strongly Asymptotically Optimal Methods for the Pathwise Global Approximation of Stochastic Differential Equations with Coefficients of Super-linear Growth"],"dc:type":["doctoralThesis"],"thesis:degree_level":["thesis.doctoral"],"thesis:institution_name":["Universität Passau"]},"updated_at":"2026-07-24T03:45:06Z"}