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2005-11-03Buch DOI: 10.18452/2586
On Halanay-type analysis of exponential stability for the theta-Maruyama method for stochastic delay differential equations
dc.contributor.authorBaker, Christopher T. H.
dc.contributor.authorBuckwar, Evelyn
dc.date.accessioned2017-06-15T17:38:23Z
dc.date.available2017-06-15T17:38:23Z
dc.date.created2005-11-03
dc.date.issued2005-11-03
dc.identifier.issn0863-0976
dc.identifier.urihttp://edoc.hu-berlin.de/18452/3238
dc.description.abstractUsing an approach that has its origins in work of Halanay, we consider stability in mean square of numerical solutions obtained from the theta-Maruyama discretization of a test stochastic delay differential equation dX(t) = {f(t) -alpha X(t) + beta X(t - tau)} {dt + {g(t) + eta X(t) + mu X (t - tau) } dW(t), interpreted in the Itô sense, where W(t) denotes a Wiener process. We focus on demonstrating that we may use techniques advanced in a recent report by Baker and Buckwar to obtain criteria for asymptotic and exponential stability, in mean square, for the solutions of the recurrence Xn+1 - Xn = theta h {fn+1 - alpha Xn+1 + beta Xn+1 - N} + + (1-theta) h {fn - alpha Xn + beta Xn-N} + sqrt{h} (gn + eta Xn + mu Xn-N) xi n (xi n in N (0,1)).eng
dc.language.isoeng
dc.publisherHumboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät II, Institut für Mathematik
dc.subjectasymptotic and exponential stabilityeng
dc.subjectstochastic delay differential \& difference equationseng
dc.subjectHalanay-type inequalitieseng
dc.subjecttheta-Maruyama schemeeng
dc.subject.ddc510 Mathematik
dc.titleOn Halanay-type analysis of exponential stability for the theta-Maruyama method for stochastic delay differential equations
dc.typebook
dc.identifier.urnurn:nbn:de:kobv:11-10052206
dc.identifier.doihttp://dx.doi.org/10.18452/2586
local.edoc.container-titlePreprints aus dem Institut für Mathematik
local.edoc.pages8
local.edoc.type-nameBuch
local.edoc.container-typeseries
local.edoc.container-type-nameSchriftenreihe
local.edoc.container-volume2004
local.edoc.container-issue14
local.edoc.container-year2004
local.edoc.container-erstkatid2075199-0

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