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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 language | English |
|---|---|
| Journal | Modern Stochastics: Theory and Applications |
| Volume | 6 |
| Issue | 2 |
| Pages (from-to) | 145-165 |
| Number of pages | 21 |
| ISSN | 2351-6046 |
| DOIs | |
| Publication status | Published - Jun 2019 |
- Chaos expansion, Malliavin calculus, numerical approximation, stochastic differential equations, EULER SCHEME, WIENER CHAOS
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