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Randomized derivative-free Milstein algorithm for efficient approximation of solutions of SDEs under noisy information

by   Paweł M. Morkisz, et al.

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 A̅^df-RM_n and investigate its error. We also study lower bounds on the error of an arbitrary algorithm. It turns out that in some case the scheme A̅^df-RM_n is the optimal one. Finally, in order to test the algorithm A̅^df-RM_n in practice, we report performed numerical experiments.


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