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2005-11-03Buch DOI: 10.18452/2597
Asymptotic mean-square stability of two-step methods for stochastic ordinary differential equations
dc.contributor.authorBuckwar, Evelyn
dc.contributor.authorHorváth-Bokor, Rosza
dc.contributor.authorWinkler, Renate
dc.date.accessioned2017-06-15T17:40:32Z
dc.date.available2017-06-15T17:40:32Z
dc.date.created2005-11-03
dc.date.issued2005-11-03
dc.identifier.issn0863-0976
dc.identifier.urihttp://edoc.hu-berlin.de/18452/3249
dc.description.abstractWe deal with linear multi-step methods for SDEs and study when the numerical appro\-xi\-mation shares asymptotic properties in the mean-square sense of the exact solution. As in deterministic numerical analysis we use a linear time-invariant test equation and perform a linear stability analysis. Standard approaches used either to analyse deterministic multi-step methods or stochastic one-step methods do not carry over to stochastic multi-step schemes. In order to obtain sufficient conditions for asymptotic mean-square stability of stochastic linear two-step-Maruyama methods we construct and apply Lyapunov-type functionals. In particular we study the asymptotic mean-square stability of stochastic counterparts of two-step Adams-Bashforth- and Adams-Moulton-methods, the Milne-Simpson method and the BDF method.eng
dc.language.isoeng
dc.publisherHumboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät II, Institut für Mathematik
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/
dc.subjectStochastic linear two-step-Maruyama methodseng
dc.subjectmean-square asymptotic stabilityeng
dc.subjectlinear stability analysiseng
dc.subjectLyapunov functionalseng
dc.subject.ddc510 Mathematik
dc.titleAsymptotic mean-square stability of two-step methods for stochastic ordinary differential equations
dc.typebook
dc.identifier.urnurn:nbn:de:kobv:11-10052315
dc.identifier.doihttp://dx.doi.org/10.18452/2597
local.edoc.container-titlePreprints aus dem Institut für Mathematik
local.edoc.pages22
local.edoc.type-nameBuch
local.edoc.container-typeseries
local.edoc.container-type-nameSchriftenreihe
local.edoc.container-volume2004
local.edoc.container-issue25
local.edoc.container-year2004
local.edoc.container-erstkatid2075199-0

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