Mean-square Convergence of Stochastic Multi-step Methods with Variable Step-size
نویسنده
چکیده
Abstract. We study mean-square consistency, stability in the mean-square sense and meansquare 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 h−ε approach and we construct some stochastic linear multi-step methods with variable step-size that have order 2 behavior if the noise is small enough.
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