The asymptotic error of chaos expansion approximations for stochastic differential equations
Volume 6, Issue 2 (2019), pp. 145–165
Pub. online: 23 April 2019
Type: Research Article
Open Access
Open Access
Received
22 November 2018
22 November 2018
Revised
9 March 2019
9 March 2019
Accepted
9 March 2019
9 March 2019
Published
23 April 2019
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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