Perturbation bounds and degree of imprecision for uniquely convergent imprecise Markov chains

TL;DR

This paper investigates how parameter perturbations affect the distributions of uniquely convergent imprecise Markov chains, providing bounds on errors and imprecision for finite and stationary distributions.

Contribution

It introduces bounds on distribution differences and imprecision degrees for perturbed imprecise Markov chains, enhancing understanding of their stability.

Findings

Derived maximal distance bounds between original and perturbed distributions.

Established bounds on errors and imprecision for finite-time and stationary distributions.

Quantified the impact of initial distribution imprecision on chain behavior.

Abstract

The effect of perturbations of parameters for uniquely convergent imprecise Markov chains is studied. We provide the maximal distance between the distributions of original and perturbed chain and maximal degree of imprecision, given the imprecision of the initial distribution. The bounds on the errors and degrees of imprecision are found for the distributions at finite time steps, and for the stationary distributions as well.