# A New Framework for Bounding Reachability Probabilities of Continuous-time Stochastic Systems

arXiv: https://arxiv.org/abs/2312.15843 · HTML: https://mlsanity.com/paper/2312.15843/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Dec 2023.

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

- [Unifying Qualitative and Quantitative Safety Verification of DNN-Controlled Systems](https://mlsanity.com/paper/2404.01769/) (2024)

## Abstract (arXiv)

This manuscript presents an innovative framework for constructing barrier functions to bound reachability probabilities for continuous-time stochastic systems described by stochastic differential equations (SDEs). The reachability probabilities considered in this paper encompass two aspects: the probability of reaching a set of specified states within a predefined finite time horizon, and the probability of reaching a set of specified states at a particular time instant. The barrier functions presented in this manuscript are developed either by relaxing a parabolic partial differential equation that characterizes the exact reachability probability or by applying the Gr"onwall's inequality. In comparison to the prevailing construction method, which relies on Doob's non-negative supermartingale inequality (or Ville's inequality), the proposed barrier functions provide stronger alternatives, complement existing methods, or fill gaps.