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The asymptotic error of chaos expansion approximations for stochastic differential equations
Volume 6, Issue 2 (2019), pp. 145–165
Tony Huschto   Mark Podolskij   Sebastian Sager  

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https://doi.org/10.15559/19-VMSTA133
Pub. online: 23 April 2019      Type: Research Article      Open accessOpen Access

Received
22 November 2018
Revised
9 March 2019
Accepted
9 March 2019
Published
23 April 2019

Abstract

In this paper we present a numerical scheme for stochastic differential equations based upon the Wiener chaos expansion. The approximation of a square integrable stochastic differential equation is obtained by cutting off the infinite chaos expansion in chaos order and in number of basis elements. We derive an explicit upper bound for the ${L^{2}}$ approximation error associated with our method. The proofs are based upon an application of Malliavin calculus.

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Keywords
Chaos expansion Malliavin calculus numerical approximation stochastic differential equations

MSC2010
65C30 60H10 60H07

Funding
This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No 647573), from Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) – 314838170, GRK 2297 MathCoRe, from the project “Ambit fields: probabilistic properties and statistical inference” funded by Villum Fonden, and from CREATES funded by the Danish National Research Foundation.

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