On classifying processes

TL;DR

This paper investigates methods for classifying stationary and ergodic processes, like Markov chains, based on successive observations, providing theoretical results to improve understanding of process membership determination.

Contribution

It offers new theoretical insights into classifying stationary ergodic processes, including Markov chains, using observational data.

Findings

Proves several results on process classification based on observations

Provides criteria for membership in classes like finite order Markov chains

Enhances understanding of process classification in ergodic theory

Abstract

We prove several results concerning classifications, based on successive observations $(X_1,..., X_n)$ of an unknown stationary and ergodic process, for membership in a given class of processes, such as the class of all finite order Markov chains.