# On the strong stability of ergodic iterations

arXiv: https://arxiv.org/abs/2304.04657 · HTML: https://mlsanity.com/paper/2304.04657/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 56 references that are in the map.
- First posted on arXiv 10 Apr 2023.

## Builds on (most cited first, 5 of 5)

- [Theoretical guarantees for approximate sampling from smooth and log-concave densities](https://mlsanity.com/paper/1412.7392/) (2014)
- [High-dimensional Bayesian inference via the Unadjusted Langevin Algorithm](https://mlsanity.com/paper/1605.01559/) (2016)
- [On stochastic gradient Langevin dynamics with dependent data streams in the logconcave case](https://mlsanity.com/paper/1812.02709/) (2018)
- [On stochastic gradient Langevin dynamics with dependent data streams: the fully non-convex case](https://mlsanity.com/paper/1905.13142/) (2019)
- [Markov chains in random environment with applications in queueing theory and machine learning](https://mlsanity.com/paper/1911.04377/) (2019)

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

- [Transition of α-mixing in Random Iterations with Applications in Queuing Theory](https://mlsanity.com/paper/2410.05056/) (2024)

## Abstract (arXiv)

We revisit processes generated by iterated random functions driven by a stationary and ergodic sequence. Such a process is called strongly stable if a random initialization exists, for which the process is stationary and ergodic, and for any other initialization, the difference between the two processes converges to zero almost surely. Under some mild conditions on the corresponding recursive map, without any condition on the driving sequence, we show the strong stability of iterations. Several applications are surveyed such as generalized autoregression and queuing. Furthermore, new results are deduced for Langevin-type iterations with dependent noise and for multitype branching processes.