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arXiv · 1912.06865

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

Paweł M. Morkisz·Paweł Przybyłowicz
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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 $\mathcal{\bar A}^{df-RM}_n$ 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 $\mathcal{\bar A}^{df-RM}_n$ is the optimal one. Finally, in order to test the algorithm $\mathcal{\bar A}^{df-RM}_n$ in practice, we report performed numerical experiments.

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Paweł M. Morkisz, Paweł Przybyłowicz. 2019-12-14. Randomized derivative-free Milstein algorithm for efficient approximation of solutions of SDEs under noisy information. https://doi.org/10.1016/j.cam.2020.113112

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