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The asymptotic error of chaos expansion approximations for stochastic differential equations

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  • Tony Huschto, Heidelberg University, Germany
  • Mark Podolskij
  • Sebastian Sager, University Magdeburg, Germany

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.

Original languageEnglish
JournalModern Stochastics: Theory and Applications
Volume6
Issue2
Pages (from-to)145-165
Number of pages21
ISSN2351-6046
DOIs
Publication statusPublished - Jun 2019

    Research areas

  • Chaos expansion, Malliavin calculus, numerical approximation, stochastic differential equations, EULER SCHEME, WIENER CHAOS

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