Non-commutative stochastic distributions and applications to linear systems theory

Abstract

In this paper, we introduce a non-commutative space of stochastic distributions, which contains the non-commutative white noise space, and forms, together with a natural multiplication, a topological algebra. A special inequality which holds in this space allows to characterize its invertible elements and to develop an appropriate framework of non-commutative stochastic linear systems.

Corrected version, to appear in Stochastic Processes and Applications