2026-09-22T14:15:59Z https://opus4.kobv.de/opus4-uni-passau/oai

oai:kobv.de-opus4-uni-passau:1963 2025-12-01 bibliography:false doc-type:PhDThesis open_access ddc ddc:519

On optimal error rates for strong approximation of stochastic differential equations with irregular drift coefficients Simon Ellinger 519 Complexity Error rates Stochastic differential equations Non-Lipschitz drift coefficient Strong approximation Lower error bounds 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. Universität Passau Passau Innstrasse 29, 94032 Passau Thomas Müller-Gronbach Larisa Yaroslavtseva Andreas Neuenkirch 2025-11-19 2025-11-27 PhDThesis Text urn:nbn:de:bvb:739-opus4-19634 application/pdf eng Creative Commons - CC BY - Namensnennung 4.0 International thesis.doctoral Universität Passau Passau Fakultät für Informatik und Mathematik 1 https://opus4.kobv.de/opus4-uni-passau/oai/container/index/docId/1963 https://opus4.kobv.de/opus4-uni-passau/frontdoor/index/index/docId/1963