For a class of unimodal maps with state-dependent dynamical and observational noise, the paper proves filter stability, a central limit theorem, and large deviations; extreme value and Poisson results are proven only when the observational noise has constant amplitude.
Thunberg, Periodicity versus Chaos in One-Dimensional Dynamics , SIAM Review 43.1 (2001), pp
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Filtering and Statistical Properties of Unimodal Maps Perturbed by Heteroscedastic Noises
For a class of unimodal maps with state-dependent dynamical and observational noise, the paper proves filter stability, a central limit theorem, and large deviations; extreme value and Poisson results are proven only when the observational noise has constant amplitude.