The Euler-Maruyama scheme for SDEs with irregular drift: Convergence rates via reduction to a quadrature problem

Neuenkirch, Andreas ; Szölgyenyi, Michaela

Document Type: Working paper
Year of publication: 2019
Place of publication: Ithaca, NY
Publishing house: Cornell University
Publication language: English
Institution: School of Business Informatics and Mathematics > Wirtschaftsmathematik II: Stochastische Numerik (Neuenkirch 2013-)
Subject: 510 Mathematics
Abstract: We study the strong convergence order of the Euler-Maruyama scheme for scalar stochastic differential equations 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. Assuming Sobolev-Slobodeckij-type regularity of order κ∈(0,1) for the drift, our analysis of the quadrature problem yields the convergence order min{3/4,(1+κ)/2}−ϵ for the equidistant Euler-Maruyama scheme (for arbitrarily small ϵ>0). The cut-off of the convergence order at κ=3/4 can be overcome by using a suitable non-equidistant discretization, which yields the strong convergence order of (1+κ)/2−ϵ for the corresponding Euler-Maruyama scheme.

Dieser Eintrag ist Teil der Universitätsbibliographie.

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