Generalized Coverage Processes with Infinitely Divisible Finite Dimensional Distributions

TL;DR

This paper introduces a new class of coverage processes with infinitely divisible distributions, generalizing classical models and including the $M/GI/\infty$ process, with theoretical limits derived from superpositions of ON/OFF Markov processes.

Contribution

It defines a novel class of coverage processes with specific correlation structures and establishes their connection to superpositions of Markov processes through limit theorems.

Findings

Processes include classical models like $M/GI/\infty$

Limit theorems for superpositions of ON/OFF Markov processes

Examples illustrating the new class of coverage processes

Abstract

In this paper we define a class of coverage processes with infinitely divisible finite dimensional distributions and a particular type of correlation structure that can be thought of as generalizations of the classical Ornstein--Uhlenbeck process and which include coverage processes such as the $M/GI/\infty$ process. We show how such processes arise naturally as limits of superpositions of independent ON/OFF Markov processes with different parameters by formulating an appropriate limit theorem. Various examples of processes of this type are given.