TBD.

Relevance to actual stochastic processes and dynamical systems, especially linear. and nonlinear system identification, and long-memory systems.

Keywords to look up:

- probability-free ergodicity
- Birkhoff ergodic theorem
- Frobenius-Perron operator
- Quasicompactness, correlation decay
- C&C CLT for Markov chains - Nagaev
- Coupling from the past

Not much material here, but please see learning theory for dependent data for some interesting categorisations of mixing and transcendence of miscellaneous mixing conditions for statistical estimators.

## Coupling from the past

Dan Piponi does a functional programming explanation of coupling from the past for markov chains.

## Mixing zoo

### \beta-mixing

### \phi-mixing

### Sequential Rademacher complexity

## Refs

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*The Annals of Statistics*, 25(1), 293–304. - PrWi98: (1998) Coupling from the past: a user’s guide. In Microsurveys in Discrete Probability (Vol. 41, pp. 181–192). Providence, Rhode Island: American Mathematical Society DOI
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