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Stochastics

The support projection of state of QMS with unbounded generator and the classical theorem for Markov chains with analytic transition semi-group

Souhir Gliouez, Skander Hachicha, Ikbel Nasraoui

Published Dec 30, 2016• 0 citations
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Abstract

We characterize the support projection of a state evolving under the action of a with unbounded generator represented in the generalized GKSL form and we give another proof of the classical Lévy-Austin-Ornstein theorem.
DOI
10.1080/17442508.2016.1267178

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We study the fundamental properties of classical and quantum Markov processes generated by q-Bessel operators and their extension to the algebra of all bounded operators on the Hilbert space [Formula: see text]. In particular, we find a suitable generalized Gorini–Kossakowski–Sudarshan–Lindblad representation for the infinitesimal generator of q-Bessel operator and show that both the classical and quantum Markov processes are transient for α > 0 and recurrent for α = 0. We also show that they do not admit invariant states and, moreover that the support projection of any initial state instantaneously fills the full space.