{"id":{"repo_id":"passau-thes","oai_identifier":"oai:kobv.de-opus4-uni-passau:1963"},"canonical_url":"https://search.dev.ndltd.org/etd/passau-thes/oai:kobv.de-opus4-uni-passau:1963","repository":{"repo_id":"passau-thes","name":"Universität Passau","base_url":"https://opus4.kobv.de/opus4-uni-passau/oai"},"display":{"title":"On optimal error rates for strong approximation of stochastic differential equations with irregular drift coefficients","abstract":"In this dissertation we study strong approximation of stochastic differential equations (SDEs) with irregular drift coefficients at the final time point or globally in time by methods that use only finitely many evaluations of the driving Brownian motion. We show the optimality of well-known methods, such as the Euler-Maruyama scheme or a transformed Milstein scheme, for classes of piecewise Lipschitz continuous, Hölder continuous and Sobolev regular drift coefficients. To do this, we derive the optimal error rates for the different classes of irregular drift coefficients. Furthermore, we show that the solution of an SDE with piecewise Hölder continuous drift coefficient has a regular local density, which is used in the proofs of the lower bounds.","abstract_html":"In this dissertation we study strong approximation of stochastic differential equations (SDEs) with irregular drift coefficients at the final time point or globally in time by methods that use only finitely many evaluations of the driving Brownian motion. We show the optimality of well-known methods, such as the Euler-Maruyama scheme or a transformed Milstein scheme, for classes of piecewise Lipschitz continuous, Hölder continuous and Sobolev regular drift coefficients. To do this, we derive the optimal error rates for the different classes of irregular drift coefficients. Furthermore, we show that the solution of an SDE with piecewise Hölder continuous drift coefficient has a regular local density, which is used in the proofs of the lower bounds.","abstract_has_math":false,"creators":["Ellinger, Simon"],"institution":"Universität Passau","degree_name":null,"degree_level":"thesis.doctoral","degree_discipline":null,"degree_department":null,"school":null,"contributors":["Müller-Gronbach, Thomas","Yaroslavtseva, Larisa","Neuenkirch, Andreas"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2025,"date_issued":"2025-11-19","date_published":"2025-11-19","updated_at":"2026-07-24T03:45:12Z","subjects":["Complexity","Error rates","Stochastic differential equations","Non-Lipschitz drift coefficient","Strong approximation","Lower error bounds"],"languages":[],"rights":["Creative Commons - CC BY - Namensnennung 4.0 International"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://opus4.kobv.de/opus4-uni-passau/frontdoor/index/index/docId/1963","outbound_label":"Repository record","outbound_source":"source_url"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Müller-Gronbach, Thomas","Yaroslavtseva, Larisa","Neuenkirch, Andreas"]},{"key":"dc:creator","label":"Author","values":["Ellinger, 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":["Complexity","Error rates","Stochastic differential equations","Non-Lipschitz drift coefficient","Strong approximation","Lower error bounds"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:rights","label":"Dc Rights","values":["Creative Commons - CC BY - Namensnennung 4.0 International"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["In this dissertation we study strong approximation of stochastic differential equations (SDEs) with irregular drift coefficients at the final time point or globally in time by methods that use only finitely many evaluations of the driving Brownian motion. We show the optimality of well-known methods, such as the Euler-Maruyama scheme or a transformed Milstein scheme, for classes of piecewise Lipschitz continuous, Hölder continuous and Sobolev regular drift coefficients. To do this, we derive the optimal error rates for the different classes of irregular drift coefficients. Furthermore, we show that the solution of an SDE with piecewise Hölder continuous drift coefficient has a regular local density, which is used in the proofs of the lower bounds."]},{"key":"dc:format.medium","label":"Dc Format Medium","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["On optimal error rates for strong approximation of stochastic differential equations with irregular drift coefficients"]}]}],"canonical_facts":{"dc:contributor":["Müller-Gronbach, Thomas","Yaroslavtseva, Larisa","Neuenkirch, Andreas"],"dc:creator":["Ellinger, Simon"],"dc:description.abstract":["In this dissertation we study strong approximation of stochastic differential equations (SDEs) with irregular drift coefficients at the final time point or globally in time by methods that use only finitely many evaluations of the driving Brownian motion. We show the optimality of well-known methods, such as the Euler-Maruyama scheme or a transformed Milstein scheme, for classes of piecewise Lipschitz continuous, Hölder continuous and Sobolev regular drift coefficients. To do this, we derive the optimal error rates for the different classes of irregular drift coefficients. Furthermore, we show that the solution of an SDE with piecewise Hölder continuous drift coefficient has a regular local density, which is used in the proofs of the lower bounds."],"dc:format.medium":["application/pdf"],"dc:publisher":["Universität Passau"],"dc:rights":["Creative Commons - CC BY - Namensnennung 4.0 International"],"dc:subject":["Complexity","Error rates","Stochastic differential equations","Non-Lipschitz drift coefficient","Strong approximation","Lower error bounds"],"dc:title":["On optimal error rates for strong approximation of stochastic differential equations with irregular drift coefficients"],"dc:type":["doctoralThesis"],"thesis:degree_level":["thesis.doctoral"],"thesis:institution_name":["Universität Passau"]},"updated_at":"2026-07-24T03:45:12Z"}