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.

Level thesis:degree_level

thesis.doctoral

Grantor dc:publisher

Universität Passau

Year

2019

Author dc:creator

• Klaus, Tina

Contributors dc:contributor

• Müller-Gronbach, Thomas
• Rößler, Andreas

Statement dc:rights

• Standardbedingung laut Einverständniserklärung

Repository record source_url

https://opus4.kobv.de/opus4-uni-passau/frontdoor/index/index/docId/766

OAI identifier oai:identifier

oai:kobv.de-opus4-uni-passau:766