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Numerical Algorithms
Erschienen in: Numerical Algorithms 1/2024

22.09.2023 | Original Paper

Convergence and stability of the Milstein scheme for stochastic differential equations with piecewise continuous arguments

verfasst von: Yuhang Zhang, Minghui Song, Mingzhu Liu, Bowen Zhao

Erschienen in: Numerical Algorithms | Ausgabe 1/2024

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Abstract

This work develops the Milstein scheme for commutative stochastic differential equations with piecewise continuous arguments (SDEPCAs), which can be viewed as stochastic differential equations with time-dependent and piecewise continuous delay. As far as we know, although there have been several papers investigating the convergence and stability for different numerical methods on SDEPCAs, all of these methods are Euler-type methods and the convergence orders do not exceed 1/2. Accordingly, we first construct the Milstein scheme for SDEPCAs in this work and then show its convergence order can reach 1. Moreover, we prove that the Milstein method can preserve the stability of SDEPCAs. In the last section, we provide several numerical examples to verify the theoretical results.
Vorheriger Artikel Enhancing multiplex global efficiency
Nächster Artikel The constant solution method for solving large-scale differential Sylvester matrix equations with time invariant coefficients

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Metadaten
Titel
Convergence and stability of the Milstein scheme for stochastic differential equations with piecewise continuous arguments
verfasst von
Yuhang Zhang
Minghui Song
Mingzhu Liu
Bowen Zhao
Publikationsdatum
22.09.2023
Verlag
Springer US
Erschienen in
Numerical Algorithms / Ausgabe 1/2024
Print ISSN: 1017-1398
Elektronische ISSN: 1572-9265
DOI
https://doi.org/10.1007/s11075-023-01652-4

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