Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4642422 | Journal of Computational and Applied Mathematics | 2008 | 20 Pages |
Abstract
We study mean-square consistency, stability in the mean-square sense and mean-square convergence of drift-implicit linear multi-step methods with variable step-size for the approximation of the solution of Itô stochastic differential equations. We obtain conditions that depend on the step-size ratios and that ensure mean-square convergence for the special case of adaptive two-step-Maruyama schemes. Further, in the case of small noise we develop a local error analysis with respect to the hh–εε approach and we construct some stochastic linear multi-step methods with variable step-size that have order 2 behaviour if the noise is small enough.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
Thorsten Sickenberger,