2026-09-22T10:39:23Z https://opus4.kobv.de/opus4-uni-passau/oai

oai:kobv.de-opus4-uni-passau:810 2025-08-13 bibliography:false doc-type:PhDThesis open_access ddc ddc:510

Strongly Asymptotically Optimal Methods for the Pathwise Global Approximation of Stochastic Differential Equations with Coefficients of Super-linear Growth 0000-0002-3119-2055 Simon Hatzesberger 510 Stochastische Differentialgleichung Approximation Stochastic differential equation Strong approximation Strong asymptotic optimality Asymptotic lower error bounds Asymptotic upper error bounds 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. Universität Passau Passau Innstrasse 29, 94032 Passau Thomas Müller-Gronbach Sotirios Sabanis 2020-02-21 2020-06-30 PhDThesis Text urn:nbn:de:bvb:739-opus4-8100 application/pdf eng Creative Commons - CC BY-SA - Namensnennung - Weitergabe unter gleichen Bedingungen 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/810 https://opus4.kobv.de/opus4-uni-passau/frontdoor/index/index/docId/810