Preprints

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Nummer 2589
Autor Debrabant, Kristian
Titel Runge-Kutta methods for third order weak approximation of SDEs with multidimensional additive noise
Upload 16.6.2009
MSC 65C30
60H35
65C20
68U20
ZDM N40
CR G.1.m
PACS 02.60.Cb
Schlüsselwörter stochastic Runge-Kutta method
stochastic differential equation
additive noise
weak approximation

Abstract:
A new class of third order Runge-Kutta methods for stochastic differential equations with additive noise is introduced. In contrast to Platen's method, which to the knowledge of the author has been up to now the only known third order Runge-Kutta scheme for weak approximation, the new class of methods affords less random variable evaluations and is also applicable to SDEs with multidimensional noise. Order conditions up to order three are calculated and coefficients of a four stage third order method are given. This method has deterministic order four and minimized error constants, and needs in addition less function evaluations than the method of Platen. Applied to a simple example, the new method is compared numerically with Platen's method and some well known second order methods and yields very promising results.

Datei:
debrabant1preprint.ps

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Verantwortliche Autorin: Anke Meier-Dörnberg

 


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