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arXiv · 1802.00888

To Numerical Modeling With Strong Orders 1.0, 1.5, and 2.0 of Convergence for Multidimensional Dynamical Systems With Random Disturbances

Dmitriy F. Kuznetsov
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Abstract

The article is devoted to explicit one-step numerical methods with strong orders 1.0, 1.5, and 2.0 of convergence for Ito stochastic differential equations with multidimensional and non-commutative noise. For numerical modeling of iterated Ito stochastic integrals with multiplicities 1 to 4 we use the method of multiple Fourier-Legendre series converging in the sense of norm in Hilbert space $L_2([t, T]^k),$ $k=1,2,3,4.$ The article is addressed to engineers who use numerical modeling in stochastic control and for solving the nonlinear filtering problem.

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Dmitriy F. Kuznetsov. 2018-02-03. To Numerical Modeling With Strong Orders 1.0, 1.5, and 2.0 of Convergence for Multidimensional Dynamical Systems With Random Disturbances. https://doi.org/10.1134/s0005117918070056

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