The asymptotic error of chaos expansion approximations for stochastic differential equations

• Verfasst von: Huschto, Tony [VerfasserIn]
• Verfasst von: Podolskij, Mark [VerfasserIn]
• Verfasst von: Sager, Sebastian [VerfasserIn]
• Titel: The asymptotic error of chaos expansion approximations for stochastic differential equations
• Verf.angabe: Tony Huschto, Mark Podolskij, Sebastian Sager
• E-Jahr: 2019
• Jahr: 23 April 2019
• Umfang: 21 S.
• Fussnoten: Gesehen am 19.06.2020
• Titel Quelle: Enthalten in: Modern stochastics: theory and applications
• Ort Quelle: [Vilnius] : VTeX, 2014
• Jahr Quelle: 2019
• Band/Heft Quelle: 6(2019), 2, Seite 145-165
• ISSN Quelle: 2351-6054
• DOI: doi:10.15559/19-vmsta133
• Datenträger: Online-Ressource
• Sprache: eng
• K10plus-PPN: 1682370089

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.