A universal dilation of discrete Markov evolutions
| dc.creator | Gregoratti, M. | |
| dc.date | 2005-12-16 | |
| dc.date.accessioned | 2026-07-07T06:55:25Z | |
| dc.date.available | 2026-07-07T06:55:25Z | |
| dc.description | Given a finite state space E, we build a universal dilation for all possible discrete time Markov chains on E, homogeneous or not: we introduce a second system (an ``environment'') and a deterministic invertible time-homogeneous global evolution of the system E with this environment such that any Markov evolution of E can be realized by a proper choice of the initial (random) state of the environment, which therefore determines the transition probabilities of the system. We also compare this dilation with the quantum dilations of a Quantum Dynamical Semigroup: 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/0512393 | |
| dc.identifier | http://arxiv.org/abs/math/0512393 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/106271 | |
| dc.subject | Probability | |
| dc.subject | 60J10; 81S25 | |
| dc.title | A universal dilation of discrete Markov evolutions | |
| dc.type | text |