2020/09/27 by Kuznetsov, Mikhail D., Kuznetsov, Dmitriy F.
#FOS: Mathematics #Probability (math.PR)
paper · doi:10.48550/arxiv.2009.14011
The article is devoted to the implementation of strong numerical methods with convergence orders 0.5, 1.0, 1.5, 2.0, 2.5, and 3.0 for Ito stochastic differential equations with multidimensional non-commutative noise based on the unified Taylor--Ito and Taylor-Stratonovich expansions and multiple Fourier-Legendre series. Algorithms for the implementation of these methods are constructed and a package of programs in the Python programming language is presented. An important part of this software package, concerning the mean-square approximation of iterated Ito and Stratonovich stochastic integrals of multiplicities 1 to 6 with respect to components of the multidimensional Wiener process is based on the method of generalized multiple Fourier series. More precisely, we used the multiple Fourier-Legendre series converging in the sense of norm in Hilbert space L2([t, T]k) (k=1,…,6) for the mean-square approximation of iterated Ito and Stratonovich stochastic integrals.