# Stochastic Contraction in Riemannian Metrics

arXiv: https://arxiv.org/abs/1304.0340 · HTML: https://mlsanity.com/paper/1304.0340/

## Key facts

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

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

- [Generalization in Supervised Learning Through Riemannian Contraction](https://mlsanity.com/paper/2201.06656/) (2022)

## Abstract (arXiv)

Stochastic contraction analysis is a recently developed tool for studying the global stability properties of nonlinear stochastic systems, based on a differential analysis of convergence in an appropriate metric. To date, stochastic contraction results and sharp associated performance bounds have been established only in the specialized context of state-independent metrics, which restricts their applicability. This paper extends stochastic contraction analysis to the case of general time- and state-dependent Riemannian metrics, in both discrete-time and continuous-time settings, thus extending its applicability to a significantly wider range of nonlinear stochastic dynamics.