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Convergence of the Euler-Maruyama method for multidimensional SDEs with discontinuous drift and degenerate diffusion coefficient

Leobacher, Gunther and Szölgyenyi, Michaela (2017) Convergence of the Euler-Maruyama method for multidimensional SDEs with discontinuous drift and degenerate diffusion coefficient. Numerische Mathematik. ISSN 0945-3245

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Abstract

We prove strong convergence of order 1/4 - E for arbitrarily small E > 0 of the Euler-Maruyama method for multidimensional stochastic differential equations (SDEs) with discontinuous drift and degenerate diffusion coefficient. The proof is based on estimating the difference between the Euler-Maruyama scheme and another numerical method, which is constructed by applying the Euler-Maruyama scheme to a transformation of the SDE we aim to solve.

Item Type: Article
Additional Information: Open access funding provided by Vienna University of Economics and Business (WU).
Keywords: Stochastic differential equations, Discontinuous drift, Degenerate Diffusion, Euler-Maruyama method, Strong convergence rate
Classification Codes: Mathematics Subject Classification Primary 60H10, 65C30, 65C20; Secondary 65L20
Divisions: Departments > Finance, Accounting and Statistics > Statistics and Mathematics
Version of the Document: Published
Depositing User: Michaela Szölgyenyi
Date Deposited: 21 Jul 2017 12:03
Last Modified: 09 Nov 2017 18:23
Related URLs:
FIDES Link: https://bach.wu.ac.at/d/research/results/78824/
URI: http://epub.wu.ac.at/id/eprint/5654

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