Multi-colored rooted tree analysis of the weak order conditions of a stochastic Runge¿Kutta family

• Autores: Yoshio Komori
• Localización: Applied numerical mathematics, ISSN-e 0168-9274, Vol. 57, Nº. 2, 2007, págs. 147-165
• Idioma: inglés
• DOI: 10.1016/j.apnum.2006.02.002
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• Resumen

  • The aim of the present paper is to give a tractable way of seeking weak order conditions of a stochastic Runge¿Kutta family for stochastic differential equations with a multi-dimensional Wiener process. This is accomplished by an extension of the rooted tree analysis for ordinary Runge¿Kutta methods. As a result, weak order conditions can be obtained directly from diagrams of multi-colored rooted trees. This new methodology will be of benefit when high weak order conditions need to be sought.