On vector-valued functional equations with multiple recursive terms

TL;DR

This paper develops a framework for solving vector-valued functional equations with multiple recursive terms, applicable to semi-Markovian queues and vector autoregressive processes.

Contribution

It introduces a detailed solution framework for complex vector-valued functional equations with recursive terms, expanding analysis tools for related stochastic models.

Findings

Framework successfully applied to semi-Markovian queueing models

Effective in analyzing vector-valued autoregressive processes

Provides theoretical insights into recursive functional equations

Abstract

In this work, we study vector-valued functional equations with multiple recursive terms that arise naturally when we are dealing with vector-valued multiplicative Lindley-type recursions. We provide a detailed framework for the solution of such equations. Our theoretical results are applied in a wide range of semi-Markovian queueing, and vector-valued autoregressive processes.