LTI Stochastic Processes: a Behavioral Perspective
For researchers in systems and control theory, this provides a foundational reinterpretation of stochastic processes, but the results are theoretical and incremental.
The paper reformulates LTI stochastic processes using a behavioral framework, deriving a canonical representation and a physically grounded notion of interconnection. It then analyzes invariance properties of distances between spectral densities.
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.