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.
Author: | Tina Klaus |
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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): | Standardbedingung laut Einverständniserklärung |