Imprecise Continuous-Time Markov Chains: Efficient Computational Methods with Guaranteed Error Bounds

TL;DR

This paper introduces improved and new efficient numerical methods for imprecise continuous-time Markov chains, enabling accurate approximations of solutions and stationary distributions with guaranteed error bounds.

Contribution

It enhances existing uniform approximation techniques and proposes a novel adaptive method, also providing a way to approximate stationary distributions with controlled error.

Findings

Enhanced uniform approximation method for better efficiency.

A new adaptive approximation approach for imprecise CTMCs.

Method to approximate stationary distributions with guaranteed error bounds.

Abstract

Imprecise continuous-time Markov chains are a robust type of continuous-time Markov chains that allow for partially specified time-dependent parameters. Computing inferences for them requires the solution of a non-linear differential equation. As there is no general analytical expression for this solution, efficient numerical approximation methods are essential to the applicability of this model. We here improve the uniform approximation method of Krak et al. (2016) in two ways and propose a novel and more efficient adaptive approximation method. For ergodic chains, we also provide a method that allows us to approximate stationary distributions up to any desired maximal error.