Autocorrelation Function Characterization of Continuous Time Markov Chains

TL;DR

This paper investigates the properties of autocorrelation functions in continuous time Markov chains, revealing conditions under which their $L^p$ norms become infinite and exploring implications for related point processes.

Contribution

It characterizes the autocorrelation functions of CTMCs, identifying conditions for infinite $L^p$ norms and deriving implications for associated point processes.

Findings

Autocorrelation functions can have infinite $L^p$ norms under certain conditions.

Properties of autocorrelation functions are linked to the structure of CTMCs.

Implications for point processes related to CTMCs are discussed.

Abstract

We study certain properties of the function space of autocorrelation functions of Unit Continuous Time Markov Chains (CTMCs). It is shown that under particular conditions, the $L^p$ norm of the autocorrelation function of arbitrary finite state space CTMCs is infinite. Several interesting inferences are made for point processes associated with CTMCs/ Discrete Time Markov Chains (DTMCs).