Dynamical and variational properties of random quantum dynamical semigroups

The random processes with values in the set of semigroups in the space of states of quantum system are studied. The mean value of such a process is the family of mean transformation which is not semigruop. The trajectories of the mean transformation family is described by 1) the pseudomeasures on the space of maps of time intervale into the coordinate space; 2) the varitional problem for the functional on the space of maps of time intervale into the space of quantum states.