# Temporal Robustness of Stochastic Signals

arXiv: https://arxiv.org/abs/2202.02583 · HTML: https://mlsanity.com/paper/2202.02583/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Feb 2022.

## Built on by (most cited first, 3 of 3)

- [Probable Domain Generalization via Quantile Risk Minimization](https://mlsanity.com/paper/2207.09944/) (2022)
- [Conformal Quantitative Predictive Monitoring of STL Requirements for Stochastic Processes](https://mlsanity.com/paper/2211.02375/) (2022)
- [Spatiotemporal Robustness of Temporal Logic Tasks using Multi-Objective Reasoning](https://mlsanity.com/paper/2603.29868/) (2026)

## Abstract (arXiv)

We study the temporal robustness of stochastic signals. This topic is of particular interest in interleaving processes such as multi-agent systems where communication and individual agents induce timing uncertainty. For a deterministic signal and a given specification, we first introduce the synchronous and the asynchronous temporal robustness to quantify the signal's robustness with respect to synchronous and asynchronous time shifts in its sub-signals. We then define the temporal robustness risk by investigating the temporal robustness of the realizations of a stochastic signal. This definition can be interpreted as the risk associated with a stochastic signal to not satisfy a specification robustly in time. In this definition, general forms of specifications such as signal temporal logic specifications are permitted. We show how the temporal robustness risk is estimated from data for the value-at-risk. The usefulness of the temporal robustness risk is underlined by both theoretical and empirical evidence. In particular, we provide various numerical case studies including a T-intersection scenario in autonomous driving.