Quantum Stochastic Processes

Abstract

A class of non-commutative stochastic processes is defined. These processes are defined up to equivalence by their multi-time correlation kernels. A reconstruction theorem, generalizing the Kolmogorov theorem for classical processes, is proved. Markov processes and their associated semigroups are studied, and some non-quasi free examples are constructed on the Clifford algebra, with the use of a perturbation theory of Markov processes. The connection with the Hepp-Lieb models is discussed.