Noncommutative dynamics and generalized master equations

作者：Belavkin V P^*

来源：Mathematical Notes, 2010, 87(5-6): 636-653.

DOI：10.1134/S0001434610050044

• quantum dynamics
• noncommutative analysis
• Girsanov transformation
• stochastic 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.

• 出版日期2010-6