✦ LIBER ✦

Mean-square convergence of stochastic multi-step methods with variable step-size

✍ Scribed by Thorsten Sickenberger

Publisher: Elsevier Science
Year: 2008
Tongue: English
Weight: 267 KB
Volume: 212
Category: Article
ISSN: 0377-0427
DOI: 10.1016/j.cam.2006.12.014

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✦ Synopsis

We study mean-square consistency, stability in the mean-square sense and mean-square convergence of drift-implicit linear multistep 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 h-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.

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