2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/98261Starting from elementary considerations about independence and Markov processes in classical probability we arrive at the new concept of conditional monotone independence (or operator-valued monotone independence). With the help of product systems of Hilbert modules we show that monotone conditional independence arises naturally in dilation theory.To appear in Proceedings of the ``First Sino-German Meeting on Stochastic Analysis'', Beijing, 2002Operator AlgebrasProbability60J25; 46L55; 46L53; 60A05text