Abstract
We deal with pointwise approximation of solutions of scalar stochastic differential equations in the presence of informational noise about underlying drift and diffusion coefficients. We define a randomized derivative-free version of Milstein algorithm Āndf−RM and investigate its error. We also study the lower bounds on the error of arbitrary algorithm. It turns out that in some case the scheme Āndf−RM is the optimal one. Finally, in order to test the algorithm Āndf−RM in practice, we report performed numerical experiments.
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