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Aufsatz / Paper in SCI-Expanded-Zeitschrift

Weak convergence of the Euler scheme for stochastic differential delay equations

Buckwar E., Kuske R., Shardlow T., Mohammed S.: Weak convergence of the Euler scheme for stochastic differential delay equations, in: LMS Journal of Computation and Mathematics, Volume 11, Page(s) 60-99, 2008.

BibTeX

@ARTICLE{
title = {Weak convergence of the Euler scheme for stochastic differential delay equations},
type = {Aufsatz / Paper in SCI-Expanded-Zeitschrift},
author = {Buckwar, Evelyn and Kuske, Rachel and Shardlow, Tony and Mohammed, Salah-Eldin},
language = {EN},
abstract = {We study weak convergence of an Euler scheme for nonlinear stochastic delay differential equations (SDDEs) driven by multidimensional Brownian motion. The Euler scheme has weak order of convergence 1, as in the case of stochastic ordinary differential equations (SODEs) (i.e., without delay). The result holds for SDDEs with multiple finite fixed delays in the drift and diffusion terms. Although the set-up is non-anticipating, our approach uses the Malliavin calculus and the anticipating stochastic analysis techniques of Nualart and Pardoux.},
pages = {60-99},
publisher = {London Mathematical Society, London},
journal = {LMS Journal of Computation and Mathematics},
volume = {11},
issn = {1461-1570},
year = {2008},
}

Details

Zusammenfassung: We study weak convergence of an Euler scheme for nonlinear stochastic delay differential equations (SDDEs) driven by multidimensional Brownian motion. The Euler scheme has weak order of convergence 1, as in the case of stochastic ordinary differential equations (SODEs) (i.e., without delay). The result holds for SDDEs with multiple finite fixed delays in the drift and diffusion terms. Although the set-up is non-anticipating, our approach uses the Malliavin calculus and the anticipating stochastic analysis techniques of Nualart and Pardoux.

Journal: LMS Journal of Computation and Mathematics
Volume: 11
Erscheinungsjahr: 2008
Seitenreferenz: 60-99
Anzahl Seiten: 40
Verlag: London Mathematical Society, London
ISSN: 1461-1570
Reichweite: International

Beteiligte

AutorInnen / HerausgeberInnen: Univ.-Prof. Dr. Evelyn Buckwar, Dr. Rachel Kuske, Dr. Tony Shardlow, Prof. Dr. Salah-Eldin Mohammed

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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