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In this paper the numerical approximation of solutions of Itô stochastic differential
equations is considered, in particular for equations with a small parameter ? in the noise coex-
cient. We construct stochastic linear multi-step methods and develop the fundamental numerical
analysis concerning their mean-square consistency, numerical stability in the mean-square sense and
mean-square convergence. For the special case of two-step Maruyama schemes we derive conditions
guaranteeing their mean-square consistency. Further, for the small noise case we obtain expansions
of the local error in terms of the stepsize and the small parameter ?. Simulation results using several
explicit and implicit stochastic linear k-step schemes, k = 1; 2, illustrate the theoretical findings.