The asymptotic error of chaos expansion approximations for stochastic differential equations
Open Access
- 23 April 2019
- journal article
- research article
- Published by VTeX in Modern Stochastics: Theory and Applications
- Vol. 6 (2), 145-165
- https://doi.org/10.15559/19-vmsta133
Abstract
Publisher: VTeX - Solutions for Science Publishing, Journal: Modern Stochastics - Theory and Applications, Title: The asymptotic error of chaos expansion approximations for stochastic differential equations, Authors: Tony Huschto, Mark Podolskij, Sebastian Sager , 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.
Keywords
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