Bvr. Bhat et Kr. Parthasarathy, MARKOV DILATIONS OF NONCONSERVATIVE DYNAMICAL SEMIGROUPS AND A QUANTUM BOUNDARY THEORY, Annales de l'I.H.P. Probabilites et statistiques, 31(4), 1995, pp. 601-651
A boundary theory for quantum Markov processes associated with noncons
ervative one parameter semigroups of completely positive linear contra
ctions on a von Neumann algebra is initiated along the lines of Feller
, Chung and Dynkin.