systems.- Construction of quantum diffusions.- The analytic continuation of a osterwalder-schrader positive representation of the euclidean group to a representation of the poincare group.- Appendix: A connection between quantum systems and stochastic processes.- Extensions of gleason theorem.- Examples of markov dilations over the 2¿ matrices.- Hamiltonian models of classical and quantum stochastic processes.- Quantum entropy and irreversibility.- Quantum ergodic theorems.- The quantum measurement process and the observation of continuous trajectories.- Generalized transition probabilities and applications.- Some remarks on quantum logics and ordered vector spaces.- A hierarchy of mixing properties for non-commutative K-systems.- Type and normality properties of some infrared representations.- Quantum theory of continuous measurements.- On the implementability of certain positive maps.- Energy versus entropy balance arguments in classical lattice systems.- Ito solution of the linear quantum stochastic differential equation describing light emission and absorption.