To Numerical Modeling With Strong Orders 1.0, 1.5, and 2.0 of Convergence for Multidimensional Dynamical Systems With Random Disturbances
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.
- Publication:
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arXiv e-prints
- Pub Date:
- February 2018
- DOI:
- 10.48550/arXiv.1802.00888
- arXiv:
- arXiv:1802.00888
- Bibcode:
- 2018arXiv180200888K
- Keywords:
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- Mathematics - Probability
- E-Print:
- 29 pages. Minor changes. arXiv admin note: text overlap with arXiv:1801.01564, arXiv:1802.00643, arXiv:1801.01962, arXiv:1801.08862, arXiv:1712.09516, arXiv:1801.03195, arXiv:1712.09746