Noncommutative dynamics and generalized master equations (Q368204)

In this paper the basic concepts of quantum probability and stochastics are reviewed using the universal Itô \(B^*\)-algebra approach. The main notions and results of classical and quantum stochastics are reformulated in this unifying approach. The general Lévy process is defined in terms of the modular \(B^*\)-Itô algebra, and the corresponding quantum stochastic master equation on the predual space of the \(W^ *\)-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 in article is also introduced.