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dc.contributor.authorIvkovic, Stefan
dc.date.accessioned2016-03-04T11:10:43Z
dc.date.available2016-03-04T11:10:43Z
dc.date.issued2015
dc.identifier.citationIvkovic, Stefan. On Markov operators and cones. Master thesis, University of Oslo, 2015
dc.identifier.urihttp://hdl.handle.net/10852/49401
dc.description.abstractIn this thesis we will consider Markov operators on cones . More precisely, we let X equipped with certain norm be a real Banach space, K in X be a closed, normal cone with nonempty interior, e in Int (K) be an order unit. A bounded, linear operator T from X into X is a Markov operator w.r.t. K and e if K is invariant under T and e is fixed by T. We consider then the adjoint of T, T* and homogeneous, discrete time Markov system given by u_k+1 = T*(u_k), k = 0,1,2 where u_0(x) is nonnegative for all x in K and u_0 (e ) = 1.The final goal of the theoretical part of this thesis is to give a sufficient on T that will guarantee the converegnce of the Markov system given above to some unique,invariant measure. This is done in theorem 6.1 which states that if T is strict contraction w.r.t. a certain norm, then this is sufficient condition for the convergence of the Markov system. The theorem states that same condition on T is also a sufficient condition for the convergence of the system x_k+1 = T(x_k) k= 0,1,2 to converge to a scalar multiple of e, so called consensus state. We apply this theorem to stochastic matricies, to Markov operators acting on the space of all continuous,real valued functions on some compact, Hausdorff topological space and to Kraus maps acting on the space of all n*n Hermitian matricies.eng
dc.language.isoeng
dc.subjectMarkov
dc.subjectoperators
dc.subjectcones
dc.subjectorder
dc.subjectunits
dc.subjectThompson
dc.subjects
dc.subjectnorm
dc.subjectHilbert
dc.subjectquotient
dc.subjectand
dc.subjectdual
dc.subjectnorm
dc.subjectsimplex
dc.titleOn Markov operators and coneseng
dc.typeMaster thesis
dc.date.updated2016-03-04T11:17:56Z
dc.creator.authorIvkovic, Stefan
dc.identifier.urnURN:NBN:no-53276
dc.type.documentMasteroppgave
dc.identifier.fulltextFulltext https://www.duo.uio.no/bitstream/handle/10852/49401/7/Stefan-Ivkovic---Master-thesis.pdf


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