NDLI: Improved linear multi-step methods for stochastic ordinary differential equations

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Improved linear multi-step methods for stochastic ordinary differential equations

Content Provider	Semantic Scholar
Author	Buckwar, Evelyn Winkler, Renate
Copyright Year	2005
Abstract	We consider linear multi-step methods for stochastic ordinary differential equations and study their convergence properties for problems with small noise or additive noise. We present schemes where the drift part is approximated by well-known methods for deterministic ordinary differential equations. Previously, we considered Maruyama-type schemes, where only the increments of the driving Wiener process are used to discretize the diffusion part. Here, we suggest to improve the discretization of the diffusion part by taking into account also mixed classical-stochastic integrals. We show that the relation of the applied step-sizes to the smallness of the noise is essential to decide whether the new methods are worth to be used. Simulation results illustrate the theoretical findings.
File Format	PDF HTM / HTML
Alternate Webpage(s)	https://edoc.hu-berlin.de/bitstream/handle/18452/3215/10.pdf?isAllowed=y&sequence=1
Alternate Webpage(s)	http://edoc.hu-berlin.de/series/mathematik-preprints/2005-10/PDF/10.pdf
Alternate Webpage(s)	http://www.math.hu-berlin.de/~winkler/papers/prep05-10.pdf
Alternate Webpage(s)	http://www.mathematik.hu-berlin.de/~buckwar/impsprep.pdf
Language	English
Access Restriction	Open
Subject Keyword	Additive white Gaussian noise Approximation algorithm Discretization Numerous Simulation Utility functions on indivisible goods
Content Type	Text
Resource Type	Article

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