# LTI Stochastic Processes: a Behavioral Perspective

## TL;DR

This paper redefines LTI stochastic processes from a behavioral perspective, providing a canonical representation and analyzing spectral density invariance, thereby deepening theoretical understanding of process interconnections.

## Contribution

It introduces a behavioral framework for LTI stochastic processes, including a canonical form and a physically grounded interconnection concept, extending prior theoretical work.

## Key findings

- Derived a canonical representation of LTI stochastic processes.
- Established a notion of interconnection grounded in physical principles.
- Analyzed invariance properties of spectral density distances.

## Abstract

This paper revisits the definition of linear time-invariant (LTI) stochastic process within a behavioral systems framework. Building on [Willems, 2013], we derive a canonical representation of an LTI stochastic process and a physically grounded notion of interconnection between independent stochastic processes. We use this framework to analyze the invariance properties enjoyed by distances between spectral densities of LTI processes.