Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4641995 | Journal of Computational and Applied Mathematics | 2008 | 15 Pages |
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.
Related Topics
Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
Kristian Debrabant, Andreas Rößler,