Non-commutative stochastic distributions and applications to linear systems theory

TL;DR

This paper develops a non-commutative space of stochastic distributions that includes white noise, forming a topological algebra, and introduces a framework for non-commutative stochastic linear systems.

Contribution

It introduces a novel non-commutative space of stochastic distributions with a natural multiplication, enabling the analysis of non-commutative stochastic linear systems.

Findings

Characterization of invertible elements in the space

Development of a framework for non-commutative stochastic linear systems

Establishment of a special inequality in the space

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.