Stability of regime-switching processes under perturbation of transition rate matrices

TL;DR

This paper investigates how regime-switching processes respond to changes in transition rate matrices, analyzing stability under different perturbation types and coefficient regularities to understand their robustness.

Contribution

It provides a comprehensive analysis of the stability of regime-switching processes under various perturbations of transition rate matrices and coefficient regularities.

Findings

Stability is maintained under fixed-size matrix perturbations.

Both regular and irregular coefficients influence stability.

Perturbations in matrix entries affect process behavior.

Abstract

This work is concerned with the stability of regime-switching processes under the perturbation of the transition rate matrices. From the viewpoint of application, two kinds of perturbations are studied: the size of the transition rate matrix is fixed, and only the values of entries are perturbed; the values of entries and the size of the transition matrix are all perturbed. Moreover, both regular and irregular coefficients of the underlying system are investigated, which clarifies the impact of the regularity of the coefficients on the stability of the underlying system.