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Aufsatz / Paper in SCI-Expanded-Zeitschrift

Continuous Θ-methods for the stochastic pantograph equation

Buckwar E., Baker C.: Continuous Θ-methods for the stochastic pantograph equation, in: ETNA. Electronic Transactions on Numerical Analysis, Volume 11, Page(s) 131-151, 2000.

BibTeX

@ARTICLE{
title = {Continuous Θ-methods for the stochastic pantograph equation},
type = {Aufsatz / Paper in SCI-Expanded-Zeitschrift},
author = {Buckwar, Evelyn and Baker, Christopher T.H. },
language = {EN},
abstract = {We consider a stochastic version of the pantograph equation: dX(t) = (aX(t) + bX(qt)) dt + (\sigma_1 + \sigma_2 X(t) + \sigma_3 X(qt))dW(t); X(0) = X0; for t \in [0; T], a given Wiener process W and 0 < q < 1. This is an example of an Itˆo stochastic delay differential equation with unbounded memory. We give the necessary analytical theory for existence and uniqueness of a strong solution of the above equation, and of strong approximations to the solution obtained by a continuous extension of the \Theta-Euler scheme (\Theta \in [0; 1]). We establish O(\sqrt{h}) mean-square convergence of approximations obtained using a bounded mesh of uniform step h, rising in the case of additive noise to O(h). Illustrative numerical examples are provided.},
pages = {131-151},
publisher = {Kent State University, Department of Mathematics and Computer Science, Kent},
journal = {ETNA. Electronic Transactions on Numerical Analysis},
volume = {11},
issn = {1068-9613},
year = {2000},
}

Details

Zusammenfassung: We consider a stochastic version of the pantograph equation: dX(t) = (aX(t) + bX(qt)) dt + (\sigma_1 + \sigma_2 X(t) + \sigma_3 X(qt))dW(t); X(0) = X0; for t \in [0; T], a given Wiener process W and 0 < q < 1. This is an example of an Itˆo stochastic delay differential equation with unbounded memory. We give the necessary analytical theory for existence and uniqueness of a strong solution of the above equation, and of strong approximations to the solution obtained by a continuous extension of the \Theta-Euler scheme (\Theta \in [0; 1]). We establish O(\sqrt{h}) mean-square convergence of approximations obtained using a bounded mesh of uniform step h, rising in the case of additive noise to O(h). Illustrative numerical examples are provided.

Journal: ETNA. Electronic Transactions on Numerical Analysis
Volume: 11
Erscheinungsjahr: 2000
Seitenreferenz: 131-151
Anzahl Seiten: 21
Verlag: Kent State University, Department of Mathematics and Computer Science, Kent
ISSN: 1068-9613
Reichweite: International

Beteiligte

AutorInnen / HerausgeberInnen: Univ.-Prof. Dr. Evelyn Buckwar, Prof. Dr. Christopher T.H. Baker

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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