Completely positive linear mappings, non-Hamiltonian evolution, and quantum stochastic processes

The present survey is mainly devoted to works published from 1969–1980 in Ref. Mat. Zh. in which completely positive linear mappings are studied that arise, in particular, in the quantum theory of open systems, the quantum theory of measurements, and in problems of the dynamics of a small system interacting with a large system. Here the probabilistic aspect is singled out, and analogies and connections with ordinary Markov processes are indicated.