Mathematics – Probability
Scientific paper
2005-12-16
Mathematics
Probability
Scientific paper
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.
No associations
LandOfFree
A universal dilation of discrete Markov evolutions does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with A universal dilation of discrete Markov evolutions, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A universal dilation of discrete Markov evolutions will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-112362