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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

Authors
  • Kuznetsov, D. F.1
  • 1 Peter the Great St. Petersburg Polytechnic University, St. Petersburg, 195251, Russia , St. Petersburg (Russia)
Type
Published Article
Journal
Computational Mathematics and Mathematical Physics
Publisher
Pleiades Publishing
Publication Date
Mar 01, 2020
Volume
60
Issue
3
Pages
379–389
Identifiers
DOI: 10.1134/S0965542520030100
Source
Springer Nature
Keywords
License
Yellow

Abstract

AbstractA 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.

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