# Asymptotic Bounds for Quantitative Verification of Perturbed Probabilistic Systems

arXiv: https://arxiv.org/abs/1304.7614 · HTML: https://mlsanity.com/paper/1304.7614/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Apr 2013.

## Built on by (most cited first, 1 of 1)

- [Leveraging System-Level Observations to Inform Bayesian Learning of Model Parameters for Quantitative Verification](https://mlsanity.com/paper/2608.03489/) (2026)

## Abstract (arXiv)

The majority of existing probabilistic model checking case studies are based on well understood theoretical models and distributions. However, real-life probabilistic systems usually involve distribution parameters whose values are obtained by empirical measurements and thus are subject to small perturbations. In this paper, we consider perturbation analysis of reachability in the parametric models of these systems (i.e., parametric Markov chains) equipped with the norm of absolute distance. Our main contribution is a method to compute the asymptotic bounds in the form of condition numbers for constrained reachability probabilities against perturbations of the distribution parameters of the system. The adequacy of the method is demonstrated through experiments with the Zeroconf protocol and the hopping frog problem.