2026-09-20T03:31:54Z https://opus4.kobv.de/opus4-uni-passau/oai

oai:kobv.de-opus4-uni-passau:766 2025-08-13 bibliography:false doc-type:PhDThesis open_access ddc ddc:510

Complexity Analysis of Quantizations of Multidimensional Stochastic Differential Equations Tina Klaus 510 Stochastische Differentialgleichung Komplexität Quantifizierung The dissertation is located in the field of quantizations of certain stochastic processes, namely a solution X of a multidimensional stochastic differential equation (SDE). The quantization problem for X consists in approximating X by a a random element which takes only finitely many values. Our main interest lies in the investigation of the asymptotic behavior of the Nth minimal quantization error of X as N tends to infinity, which incorporates the determination of both the sharp rate of convergence and explicit asymptotic constants. Especially explicit asymptotic constants have been so far unknown in the context of multidimensional SDEs. Furthermore, as part of our analysis, we provide a method which yields a strongly asymptotically optimal sequence of N-quantization of X. In certain special cases our method is fully constructive and the algorithm is easy to implement. Universität Passau Passau Innstrasse 29, 94032 Passau Thomas Müller-Gronbach Andreas Rößler 2019-02-21 2020-01-10 PhDThesis Text urn:nbn:de:bvb:739-opus4-7665 application/pdf eng Standardbedingung laut Einverständniserklärung thesis.doctoral Universität Passau Passau Fakultät für Informatik und Mathematik 1 https://opus4.kobv.de/opus4-uni-passau/oai/container/index/docId/766 https://opus4.kobv.de/opus4-uni-passau/frontdoor/index/index/docId/766