Monotone quantum stochastic processes and covariant dynamical hemigroups ✩

Based on the Hilbert C∗-module structure we study non-stationary monotone quantum stochastic processes and generalMarkov processes constructed from quantum dynamical hemigroups indexed by a totally ordered set. We prove that the quantum stochastic monotone process implementing the weakly covariant process described by a covariant quantum dynamical hemigroup with respect to a symmetry semigroup is again covariant in the strong sense. © 2011 Elsevier Inc. All rights reserved