Classical dilations à la Hudson-Parthasarathy of Markov semigroups

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dc.creatorGregoratti, M.
dc.date2007-02-26
dc.date.accessioned2026-07-07T09:59:48Z
dc.date.available2026-07-07T09:59:48Z
dc.descriptionWe study the Classical Probability analogue of the dilations of a quantum dynamical semigroup defined in Quantum Probability via quantum stochastic differential equations. Given a homogeneous Markov chain in continuous time in a finite state space E, we introduce a second system, an environment, and a deterministic invertible time-homogeneous global evolution of the system E with this environment such that the original Markov evolution of E can be realized by a proper choice of the initial random state of the environment. We also compare this dilations with the dilations of a quantum dynamical semigroup in Quantum Probability: given a classical Markov semigroup, we extend it to a proper quantum dynamical semigroup for which we can find a Hudson-Parthasarathy dilation which is itself an extension of our classical dilation.
dc.identifierhttps://arxiv.org/abs/math/0702784
dc.identifierhttp://arxiv.org/abs/math/0702784
dc.identifierStochastic Analysis and Applications, Volume 26, Issue 5 September 2008, pages 1025 - 1052
dc.identifierdoi:10.1080/07362990802286475
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/168154
dc.subjectProbability
dc.subject60J27; 81S25
dc.titleClassical dilations à la Hudson-Parthasarathy of Markov semigroups
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