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Aufsatz / Paper in SCI-Expanded-Zeitschrift

Asymptotic mean-square stability of two-step methods for stochastic ordinary differential equations

Buckwar E., Horváth-Bokor R., Winkler R.: Asymptotic mean-square stability of two-step methods for stochastic ordinary differential equations, in: BIT Numerical Mathematics, Volume 46, Number 2, Page(s) 261-282, 2006.

BibTeX

@ARTICLE{
title = {Asymptotic mean-square stability of two-step methods for stochastic ordinary differential equations},
type = {Aufsatz / Paper in SCI-Expanded-Zeitschrift},
author = {Buckwar, Evelyn and Horváth-Bokor, Rozsa and Winkler, Renate},
language = {EN},
abstract = {We deal with linear multi-step methods for SDEs and study when the numerical approximation shares asymptotic properties in the mean-square sense of the exact solution. As in deterministic numerical analysis we use a linear time-invariant test equation and perform a linear stability analysis. Standard approaches used either to analyse deterministic multi-step methods or stochastic one-step methods do not carry over to stochastic multi-step schemes. In order to obtain sufficient conditions for asymptotic mean-square stability of stochastic linear two-step-Maruyama methods we construct and apply Lyapunov-type functionals. In particular we study the asymptotic mean-square stability of stochastic counterparts of two-step Adams–Bashforth- and Adams–Moulton-methods, the Milne–Simpson method and the BDF method.},
pages = {261-282},
publisher = {Springer, Dordrecht},
journal = {BIT Numerical Mathematics},
volume = {46},
number = {2},
issn = {0006-3835},
year = {2006},
}

Details

Zusammenfassung: We deal with linear multi-step methods for SDEs and study when the numerical approximation shares asymptotic properties in the mean-square sense of the exact solution. As in deterministic numerical analysis we use a linear time-invariant test equation and perform a linear stability analysis. Standard approaches used either to analyse deterministic multi-step methods or stochastic one-step methods do not carry over to stochastic multi-step schemes. In order to obtain sufficient conditions for asymptotic mean-square stability of stochastic linear two-step-Maruyama methods we construct and apply Lyapunov-type functionals. In particular we study the asymptotic mean-square stability of stochastic counterparts of two-step Adams–Bashforth- and Adams–Moulton-methods, the Milne–Simpson method and the BDF method.

Journal: BIT Numerical Mathematics
Volume: 46
Nummer: 2
Erscheinungsjahr: 2006
Seitenreferenz: 261-282
Anzahl Seiten: 22
Verlag: Springer, Dordrecht
ISSN: 0006-3835
Reichweite: International

Beteiligte

AutorInnen / HerausgeberInnen: Univ.-Prof. Dr. Evelyn Buckwar, Dr Rozsa Horváth-Bokor, Dr. Renate Winkler

Forschungseinheiten der JKU:

Wissenschaftszweige: 1103 Analysis | 1113 Mathematische Statistik | 1114 Numerische Mathematik | 1118 Wahrscheinlichkeitstheorie | 1121 Operations Research | 1145 Zeitreihenanalyse | 1165 Stochastik | 5943 Risikoforschung

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