Vorlesen

Research Seminar Series in Statistics and Mathematics

Wirtschaftsuniversität Wien , Departments 4 D4.4.008 09:00 - 10:30

Art Vortrag/Diskussion
SpracheEnglish
Vortragende/rMichaela Szölgyenyi (Department of Statistics, University of Klagenfurt)
Veranstalter Institut für Statistik und Mathematik
Kontakt katrin.artner@wu.ac.at

Michaela Szölgyenyi (Department of Statistics, University of Klagenfurt) about "Convergence order of Euler-type schemes for SDEs in dependence of the Sobolev regularity of the drift"

The Institute for Statistics and Mathematics (Department of Finance, Accounting and Statistics) cordially invites everyone interested to attend the talks in our Research Seminar Series, where internationally renowned scholars from leading universities present and discuss their (working) papers.
No registration required.

The list of talks for the summer term 2019 is available via the following link: https://www.wu.ac.at/en/statmath/resseminar

Abstract:
Stochastic differential equations with irregular (non-globally Lipschitz) coefficients are a very active topic of research. We study the strong convergence rate of the Euler-Maruyama scheme for scalar SDEs with additive noise and irregular drift. We provide a novel framework for the error analysis by reducing it to a weighted quadrature problem for irregular functions of Brownian motion. By analysing the quadrature problem we obtain for arbitrarily small ε > 0 a strong convergence order of (1+κ)/2–ε for a non-equidistant Euler-Maruyama scheme, if the drift has Sobolev-Slobodeckij-type regularity of order κ. In the multi-dimensional setting we allow the drift coefficient to be non-Lipschitz on a set of positive reach. We prove strong convergence of an Euler-type scheme, which uses adaptive step-sizing for a better resolution close to the discontinuity. We obtain a numerical method which has – up to logarithmic terms – strong convergence order 1/2 with respect to the average computational cost.



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