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Avtomat. i Telemekh., 2019, Issue 5, Pages 99–117 (Mi at15281)  

Stochastic Systems

On numerical modeling of the multidimentional dynamic systems under random perturbations with the 2.5 order of strong convergence

D. F. Kuznetsov

Peter the Great St. Petersburg Polytechnic University, St. Petersburg, Russia

Abstract: Numerical modeling methods with a strong convergence of order 2.5 are developed for the multidimensional dynamic systems under random perturbations described by Itô stochastic differential equations. Special attention is paid to the numerical modeling methods of the multiple Itô stochastic integrals of multiplicities 1–5 in terms of the mean-square convergence criterion, which are required to implement the former methods.

Keywords: multiple Itô stochastic integral, Fourier series, numerical method, mean-square convergence.

DOI: https://doi.org/10.1134/S0005231019050064

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English version:
Automation and Remote Control, 2019, 80:5, 867–881

Bibliographic databases:

Document Type: Article
Presented by the member of Editorial Board: B. M. Miller

Received: 15.07.2018
Revised: 02.11.2018
Accepted: 08.11.2018

Citation: D. F. Kuznetsov, “On numerical modeling of the multidimentional dynamic systems under random perturbations with the 2.5 order of strong convergence”, Avtomat. i Telemekh., 2019, no. 5, 99–117; Autom. Remote Control, 80:5 (2019), 867–881

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