Abstract
A convergence theorem for the continuous weak approximation of the solution of stochastic differential equations (SDEs) by general one-step methods is proved, which is an extension of a theorem due to Milstein. As an application, uniform second order conditions for a class of continuous stochastic Runge-Kutta methods containing the continuous extension of the second order stochastic Runge-Kutta scheme due to Platen are derived. Further, some coefficients for optimal continuous schemes applicable to Itô SDEs with respect to a multi-dimensional Wiener process are presented.
Original language | English |
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Journal | Journal of Computational and Applied Mathematics |
Volume | 214 |
Issue number | 1 |
Pages (from-to) | 259-273 |
Number of pages | 15 |
ISSN | 0377-0427 |
DOIs | |
Publication status | Published - 15.04.2008 |