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.
Sequential Rademacher complexity
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