On Obtaining Sharp Bounds of the Rate of Convergence for a Class of Continuous-Time Markov Chains

TL;DR

This paper investigates inhomogeneous continuous-time Markov chains with finite states, introducing a class with regular infinitesimal matrices and deriving sharp bounds on their convergence rates.

Contribution

It defines a new class of Markov chains with regular infinitesimal matrices and establishes precise upper bounds on their convergence speed.

Findings

Established sharp upper bounds for convergence rates.

Identified conditions for regular structure of infinitesimal matrices.

Enhanced understanding of ergodic behavior in finite-state Markov chains.

Abstract

We study inhomogeneous continuous-time weakly ergodic Markov chains with a finite state space. We introduce the notion of a Markov chain with the regular structure of an infinitesimal matrix and study the sharp upper bounds on the rate of convergence for such class of Markov chains.