Stochastic properties of dynamical
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Stochastic properties of dynamical
This book provides an introduction to the study of the stochastic properties of probability preserving dynamical systems. Only the usual knowledge of the first year of a Master's degree is required. Many reminders are given. The definitions and results are illustrated by examples anc corrected exercises. The book presents the notions of Poincaré's recurrence, of ergodicity, of mixing. It enlights also existing lonks between dynamical systems and Markov chains.
The final objective of this books is to present three methods for establishing central limit theorems in the context of chaotic dynamical systems : a first method based on martingale approximations, a second method based on perturbation of quasi-compact linear operators and a third method on decorrelation estimates.
The final objective of this books is to present three methods for establishing central limit theorems in the context of chaotic dynamical systems : a first method based on martingale approximations, a second method based on perturbation of quasi-compact linear operators and a third method on decorrelation estimates.
This book provides an introduction to the study of the stochastic properties of probability preserving dynamical systems. Only the usual knowledge of the first year of a Master's degree is required. Many reminders are given. The definitions and results are illustrated by examples anc corrected exercises. The book presents the notions of Poincaré's recurrence, of ergodicity, of mixing. It enlights also existing lonks between dynamical systems and Markov chains.
The final objective of this books is to present three methods for establishing central limit theorems in the context of chaotic dynamical systems : a first method based on martingale approximations, a second method based on perturbation of quasi-compact linear operators and a third method on decorrelation estimates.
The final objective of this books is to present three methods for establishing central limit theorems in the context of chaotic dynamical systems : a first method based on martingale approximations, a second method based on perturbation of quasi-compact linear operators and a third method on decorrelation estimates.
