Abstract
A general class of stochastic Runge-Kutta methods for the weak approximation of Itô and Stratonovich stochastic differential equations with a multi-dimensional Wiener process is introduced. Colored rooted trees are used to derive an expansion of the solution process and of the approximation process calculated with the stochastic Runge-Kutta method. A theorem on general order conditions for the coefficients and the random variables of the stochastic Runge-Kutta method is proved by rooted tree analysis. This theorem can be applied for the derivation of stochastic Runge-Kutta methods converging with an arbitrarily high order.
Original language | English |
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Journal | Stochastic Analysis and Applications |
Volume | 24 |
Issue number | 1 |
Pages (from-to) | 97-134 |
Number of pages | 38 |
ISSN | 0736-2994 |
DOIs | |
Publication status | Published - 01.03.2006 |