On optimal error rates for strong approximation of stochastic differential equations with irregular drift coefficients

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.

Level thesis:degree_level

thesis.doctoral

Grantor dc:publisher

Universität Passau

Year

2025

Author dc:creator

• Ellinger, Simon

Contributors dc:contributor

• Müller-Gronbach, Thomas
• Yaroslavtseva, Larisa
• Neuenkirch, Andreas

• Complexity
• Error rates
• Stochastic differential equations
• Non-Lipschitz drift coefficient
• Strong approximation
• Lower error bounds

Statement dc:rights

• Creative Commons - CC BY - Namensnennung 4.0 International

Repository record source_url

https://opus4.kobv.de/opus4-uni-passau/frontdoor/index/index/docId/1963

OAI identifier oai:identifier

oai:kobv.de-opus4-uni-passau:1963