On the Rate of Convergence for a Characteristic of Multidimensional Birth-Death Process

TL;DR

This paper investigates the convergence rates of multidimensional inhomogeneous birth-death processes by deriving bounds for the convergence of their associated one-dimensional processes.

Contribution

It provides new bounds on the convergence rate of multidimensional birth-death processes, extending understanding of their long-term behavior.

Findings

Derived bounds on convergence rates for one-dimensional processes

Extended results to multidimensional inhomogeneous birth-death processes

Enhanced theoretical understanding of process stability

Abstract

We consider a multidimensional inhomogeneous birth-death process (BDP) and obtain bounds on the rate of convergence for the corresponding one-dimensional processes.