Covariant Markov dilations of quantum dynamical semigroups (Q1076435)

The dilation problem for completely positive quantum dynamical semigroups is studied in algebraic framework of the theory of quantum stochastic processes. The general scheme of the so-called covariant Markov \(W^*\)- stochastic processes which are unitary dilations of the associated dynamical semigroup is developed. Explicit constructions of such processes are obtained using the non-commutative stochastic calculus of Hudson and Parthasarathy.