Instrumental processes, entropies, information in quantum continual measurements

In this paper we give a short presentation of the quantum Levy-Khinchin formula and of the formulation of quantum continual measurements based on stochastic differential equations, matters which we had the pleasure to work on in collaboration with Prof. Holevo. Then we begin the study of various entropies and relative entropies, which seem to be promising quantities for measuring the information content of the continual measurement under consideration and for analysing its asymptotic behaviour.