English

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

Probability 2022-09-13 v6

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 L2([t,T]k),L_2([t, T]^k), k=1,2,3,4.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.

Keywords

Cite

@article{arxiv.1802.00888,
  title  = {To Numerical Modeling With Strong Orders 1.0, 1.5, and 2.0 of Convergence for Multidimensional Dynamical Systems With Random Disturbances},
  author = {Dmitriy F. Kuznetsov},
  journal= {arXiv preprint arXiv:1802.00888},
  year   = {2022}
}

Comments

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