Noncommutative dynamics and generalized master equations

We review the basic concepts of quantum probability and stochastics using the universal It B*-algebra approach. The main notions and results of classical and quantum stochastics are reformulated in this unifying approach. The general L,vy process is defined in terms of the modular B*-It algebra, and the corresponding quantum stochastic master equation on the predual space of theW*-algebra is derived as a noncommutative version of the Zakai equation driven by the process. This is done by a noncommutative analog of the Girsanov transformation, which we introduce here in full generality.