Classification of stochastic Runge-Kutta methods for the weak approximation of stochastic differential equations

Kristian Debrabant*, Andreas Rößler

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

Abstract

In the present paper, a class of stochastic Runge-Kutta methods containing the second order stochastic Runge-Kutta scheme due to E. Platen for the weak approximation of Itô stochastic differential equation systems with a multi-dimensional Wiener process is considered. Order 1 and order 2 conditions for the coefficients of explicit stochastic Runge-Kutta methods are solved and the solution space of the possible coefficients is analyzed. A full classification of the coefficients for such stochastic Runge-Kutta schemes of order 1 and two with minimal stage numbers is calculated. Further, within the considered class of stochastic Runge-Kutta schemes coefficients for optimal schemes in the sense that additionally some higher order conditions are fulfilled are presented.

OriginalspracheEnglisch
ZeitschriftMathematics and Computers in Simulation
Jahrgang77
Ausgabenummer4
Seiten (von - bis)408-420
Seitenumfang13
ISSN0378-4754
DOIs
PublikationsstatusVeröffentlicht - 04.04.2008

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