Classical dilations à la Quantum Probability of Markov evolutions in discrete time
| dc.creator | Gregoratti, M. | |
| dc.date | 2007-02-23 | |
| dc.date.accessioned | 2026-07-07T07:48:29Z | |
| dc.date.available | 2026-07-07T07:48:29Z | |
| dc.description | We study the Classical Probability analogue of the dilations of a quantum dynamical semigroup in Quantum Probability. Given a (not necessarily homogeneous) Markov chain in discrete 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 show that it can be extended to a quantum dynamical semigroup for which we can find a quantum dilation to a group of *-automorphisms admitting an invariant abelian subalgebra where this quantum dilation gives just our classical dilation. | |
| dc.identifier | https://arxiv.org/abs/math/0702690 | |
| dc.identifier | http://arxiv.org/abs/math/0702690 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/124517 | |
| dc.subject | Probability | |
| dc.subject | 60J10 (Primary); 81S25 (Secondary) | |
| dc.title | Classical dilations à la Quantum Probability of Markov evolutions in discrete time | |
| dc.type | text |