Seitenbereiche:



Zusatzinformationen:

FUN-Veranstaltungen

FoFö-Stammtisch, 23. November 2017, 14 Uhr siehe Info-Veranstaltungen

Kontakt

Abteilung Forschungsunterstützung (FUN):
forschen@jku.at


Positionsanzeige:

Inhalt:

Forschungseinheiten

Aufsatz / Paper in SCI-Expanded-Zeitschrift

Runge-Kutta methods for jump-diffusion differential equations

Buckwar E., Riedler M.: Runge-Kutta methods for jump-diffusion differential equations, in: Journal of Computational and Applied Mathematics, Volume 236, Number 6, Page(s) 1155-1182, 2011.

BibTeX

@ARTICLE{
title = {Runge-Kutta methods for jump-diffusion differential equations},
type = {Aufsatz / Paper in SCI-Expanded-Zeitschrift},
author = {Buckwar, Evelyn and Riedler, Martin},
language = {EN},
abstract = {In this paper we consider Runge-Kutta methods for jump-diffusion differential equations. We present a study of their mean-square convergence properties for problems with multiplicative noise. We are concerned with two classes of Runge-Kutta methods. First, we analyse schemes where the drift is approximated by a Runge-Kutta ansatz and the diffusion and jump part by a Maruyama term and second we discuss improved methods where mixed stochastic integrals are incorporated in the approximation of the next time step as well as the stage values of the Runge-Kutta ansatz for the drift. The second class of methods are specifically developed to improve the accuracy behaviour of problems with small noise. We present results showing when the implicit stochastic equations defining the stage values of the Runge-Kutta methods are uniquely solvable. Finally, simulation results illustrate the theoretical findings.},
pages = {1155-1182},
publisher = {Elsevier Science B.V. (North Holland), Amsterdam},
journal = {Journal of Computational and Applied Mathematics},
volume = {236},
number = {6},
issn = {0377-0427},
month = {10},
year = {2011},
url = {http://www.sciencedirect.com/science/article/pii/S0377042711004407},
}

Details

Zusammenfassung: In this paper we consider Runge-Kutta methods for jump-diffusion differential equations. We present a study of their mean-square convergence properties for problems with multiplicative noise. We are concerned with two classes of Runge-Kutta methods. First, we analyse schemes where the drift is approximated by a Runge-Kutta ansatz and the diffusion and jump part by a Maruyama term and second we discuss improved methods where mixed stochastic integrals are incorporated in the approximation of the next time step as well as the stage values of the Runge-Kutta ansatz for the drift. The second class of methods are specifically developed to improve the accuracy behaviour of problems with small noise. We present results showing when the implicit stochastic equations defining the stage values of the Runge-Kutta methods are uniquely solvable. Finally, simulation results illustrate the theoretical findings.

Journal: Journal of Computational and Applied Mathematics
Volume: 236
Nummer: 6
Erscheinungsjahr: 2011
Seitenreferenz: 1155-1182
Anzahl Seiten: 28
Web: http://www.sciencedirect.com/science/article/pii/S0377042711004407 (Article)
DOI: http://dx.doi.org/10.1016/j.cam.2011.08.001
Verlag: Elsevier Science B.V. (North Holland), Amsterdam
ISSN: 0377-0427
Reichweite: International

Beteiligte

AutorInnen / HerausgeberInnen: Univ.-Prof. Dr. Evelyn Buckwar, DI Ph.D. Martin Riedler

Forschungseinheiten der JKU:

Wissenschaftszweige: 1103 Analysis | 1114 Numerische Mathematik | 1118 Wahrscheinlichkeitstheorie | 1165 Stochastik

Zurück Zurück