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Complexity Analysis of Quantizations of Multidimensional Stochastic Differential Equations

  • 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.

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Metadaten
Author:Tina Klaus
URN:urn:nbn:de:bvb:739-opus4-7665
Advisor:Thomas Müller-Gronbach, Andreas Rößler
Document Type:Doctoral Thesis
Language:English
Year of Completion:2019
Date of Publication (online):2020/01/10
Date of first Publication:2020/01/10
Publishing Institution:Universität Passau
Granting Institution:Universität Passau, Fakultät für Informatik und Mathematik
Date of final exam:2019/02/21
Release Date:2020/01/10
GND Keyword:Stochastische Differentialgleichung; Komplexität; Quantifizierung
Page Number:iv, 166 Seiten
Institutes:Fakultät für Informatik und Mathematik
Dewey Decimal Classification:5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik
open_access (DINI-Set):open_access
Licence (German):License LogoStandardbedingung laut Einverständniserklärung