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2005-03-10Buch DOI: 10.18452/2553
Solutions of affine stochastic functional differential equations in the state space
dc.contributor.authorRiedle, Markus
dc.date.accessioned2017-06-15T17:31:58Z
dc.date.available2017-06-15T17:31:58Z
dc.date.created2005-11-02
dc.date.issued2005-03-10
dc.identifier.issn0863-0976
dc.identifier.urihttp://edoc.hu-berlin.de/18452/3205
dc.description.abstractIn this article we consider solutions of affine stochastic functional differential equations. The drift of these equations is specified by a functional defined on a general function space B which is only described axiomatically. The solutions are reformulated as stochastic processes in the space B. By representing such a process in the bidual space of B we establish that the transition functions of this process form a generalized Gaussian Mehler semigroup on B. Thus the process is characterized completely on B since it is Markovian. Moreover we derive a sufficient and necessary condition on the underlying space B such that the transition functions are even an Ornstein-Uhlenbeck semigroup. We exploit this result to associate a Cauchy problem in the function space B to the finite-dimensional functional equation.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 integral equationseng
dc.subjectStochastic delay equationseng
dc.subjectGaussian processeseng
dc.subjectTransition functionseng
dc.subjectgenerators and resolventseng
dc.subject.ddc510 Mathematik
dc.titleSolutions of affine stochastic functional differential equations in the state space
dc.typebook
dc.identifier.urnurn:nbn:de:kobv:11-10051736
dc.identifier.doihttp://dx.doi.org/10.18452/2553
local.edoc.container-titlePreprints aus dem Institut für Mathematik
local.edoc.pages28
local.edoc.type-nameBuch
local.edoc.container-typeseries
local.edoc.container-type-nameSchriftenreihe
local.edoc.container-volume2005
local.edoc.container-issue3
local.edoc.container-year2005
local.edoc.container-erstkatid2075199-0

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