Explicit One-Step Numerical Method with the Strong Convergence Order of 2.5 for Ito Stochastic Differential Equations with a Multi-Dimensional Nonadditive Noise Based on the Taylor–Stratonovich Expansion
Abstract
A strongly converging method of order 2.5 for Ito stochastic differential equations with multidimensional nonadditive noise based on the unified Taylor–Stratonovich expansion is proposed. The focus is on the approaches and methods of mean square approximation of iterated Stratonovich stochastic integrals of multiplicities 1–5 the numerical simulation of which is the main difficulty in the implementation of the proposed numerical method.
- Publication:
-
Computational Mathematics and Mathematical Physics
- Pub Date:
- March 2020
- DOI:
- 10.1134/S0965542520030100
- arXiv:
- arXiv:1806.10705
- Bibcode:
- 2020CMMPh..60..379K
- Keywords:
-
- multiple Fourier-Legendre series;
- iterated Ito stochastic integral;
- iterated Stratonovich stochastic integral;
- Ito stochastic differential equation;
- Taylor-Stratonovich expansion;
- multiple Fourier–Legendre series;
- Taylor–Stratonovich expansion;
- Mathematics - Probability
- E-Print:
- 29 pages. Minor changes. arXiv admin note: substantial text overlap with arXiv:1712.08991, arXiv:1802.04844, arXiv:1901.02345, arXiv:1712.09516, arXiv:1801.01564, arXiv:1802.00643, arXiv:1805.12527, arXiv:1801.00231, arXiv:1801.05654, arXiv:1801.03195