On the structure of Markov flows

A new infinitesimal characterization of completely positive but not necessa rily homomorphic Markov flows from a C-*-algebra to bounded operators on th e boson Fock space over L-2(R) is given. Contrarily to previous characteriz ations, based on stochastic differential equations, this characterization i s universal, i.e., valid for arbitrary Markov flows. With this result the s tudy of Markov flows is reduced to the study of four C-0-semigroups. This i ncludes the classical case and even in this case it seems to be new. The re sult is applied to deduce a new existence theorem for Markov flows. (C) 200 1 Elsevier Science Ltd. All rights reserved.