Runge-Kutta methods for the strong approximation of solutions of stochastic differential equations

Andreas Rößler*

*Korrespondierende/r Autor/-in für diese Arbeit
50 Zitate (Scopus)

Abstract

Some new stochastic Runge-Kutta (SRK) methods for the strong approximation of solutions of stochastic differential equations (SDEs) with improved efficiency are introduced. Their convergence is proved by applying multicolored rooted tree analysis. Order conditions for the coefficients of explicit and implicit SRK methods are calculated. As the main novelty, order 1.0 strong SRK methods with significantly reduced computational complexity for Itô as well as for Stratonovich SDEs with a multidimensional driving Wiener process are presented where the number of stages is independent of the dimension of the Wiener process. Further, an order 1.0 strong SRK method customized for Itô SDEs with commutative noise is introduced. Finally, some order 1.5 strong SRK methods for SDEs with scalar, diagonal, and additive noise are proposed. All introduced SRK methods feature significantly reduced computational complexity compared to well-known schemes.

OriginalspracheEnglisch
ZeitschriftSIAM Journal on Numerical Analysis
Jahrgang48
Ausgabenummer3
Seiten (von - bis)922-952
Seitenumfang31
ISSN0036-1429
DOIs
PublikationsstatusVeröffentlicht - 01.09.2010

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