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

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:383

Article

Morkisz, Pawel M.^1,2  Przybylowicz, Pawel¹ 

[1] AGH Univ Sci & Technol, Fac Appl Math, Al A Mickiewcza 30, PL-30059 Krakow, Poland

[2] NVIDIA Poland, Warsaw, Poland

关键词: SDEs;    Standard noisy information;    Pointwise approximation;    Randomized Milstein algorithm;    nth minimal error;    Optimality;   

DOI  :  10.1016/j.cam.2020.113112

来源: Elsevier

【 摘 要 】

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 A(n)(-df-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 A(n)(-df-RM ) is the optimal one. Finally, in order to test the algorithm A(n)(-df-RM ) in practice, we report performed numerical experiments. (C) 2020 Elsevier B.V. All rights reserved.

【 授权许可】

Free