Mathematics – Probability
Scientific paper
2007-02-26
Stochastic Analysis and Applications, Volume 26, Issue 5 September 2008, pages 1025 - 1052
Mathematics
Probability
Scientific paper
10.1080/07362990802286475
We 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.
No associations
LandOfFree
Classical dilations à la Hudson-Parthasarathy of Markov semigroups 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 Classical dilations à la Hudson-Parthasarathy of Markov semigroups, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Classical dilations à la Hudson-Parthasarathy of Markov semigroups will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-131820