## Vector-valued almost sure invariance principles for (non)stationary and random dynamical systems

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**375**(2022), 4809-4848 Request permission

## Abstract:

We study the limit behavior of (non)stationary and random chaotic dynamical systems. Several (vector-valued) almost sure invariance principles for (non)stationary dynamical systems and quenched (vector-valued) almost sure invariance principles for random dynamical systems are proved. We also apply our results to stationary chaotic dynamical systems, which admit Young towers, and to (non)uniformly expanding non-stationary and random dynamical systems with intermittencies or uniform spectral gaps. It implies that the systems under study tend to a Brownian motion under various scalings.## References

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## Additional Information

**Yaofeng Su**- Affiliation: School of Mathematics, Georgia Institute of Technology, Atlanta, Georgia
- MR Author ID: 1346523
- Email: yaofeng.su@math.gatech.edu
- Received by editor(s): May 1, 2020
- Received by editor(s) in revised form: March 31, 2021, May 29, 2021, August 4, 2021, November 12, 2021, and November 18, 2021
- Published electronically: March 16, 2022
- © Copyright 2022 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**375**(2022), 4809-4848 - MSC (2020): Primary 37C99
- DOI: https://doi.org/10.1090/tran/8609
- MathSciNet review: 4439492