Mixing

1. General properties.- 1.1. Dependence of ?-fields.- 1.2. Basic tools.- 1.2.1. Reconstruction techniques.- 1.2.2. Covariance inequalities.- 1.3. Mixing.- 1.3.1. Mixing random fields.- 1.3.2. Mixing processes.- 1.3.3. Weak conditions for processes.- 1.3.4. Miscellany.- 1.4. Tools.- 1.4.1. Moment inequalities.- 1.4.2. Exponential inequalities.- 1.4.3. Maximal inequalities.- 1.5. Central limit theorem.- 1.5.1 Sufficient conditions.- 1.5.2. Convergence rates.- 1.5.3. Dimension dependent rates.- 2. Examples.- 2.1. Gaussian random fields.- 2.1.1. An explicit bound.- 2.1.2. Mixing rates.- 2.2. Gibbs fields.- 2.2.1 Dobrushin theory.- 2.2.1.1. Comparison between specifications.- 2.2.1.2 Dobrushin’s condition.- 2.2.1.3. Mixing condition.- 2.2.2 Markov fields.- 2.2.2.1. Potentials.- 2.2.3 Non compact case.- 2.2.3.1. Point processes.- 2.2.3.2. Diffusions.- 2.3. Linear fields.- 2.3.1. Independent innovations.- 2.3.2. Dependent innovations.- 2.3.3. Proofs.- 2.3.4. Miscellany.- 2.4. Markov processes.- 2.4.0.1. A class of non linear models.- 2.4.0.2. Dynamical systems approach.- 2.4.0.3. Annealing.- 2.4.1. Polynomial AR processes.- 2.4.1.1. Bilinear models.- 2.4.1.2. ARMA models.- 2.4.2. Nonlinear processes.- 2.4.2.1. ARX(k, q) nonlinear processes.- 2.4.2.2. AR(1) nonlinear processes.- 2.4.2.3. Financial nonlinear processes.- 2.5. Continuous time processes.- 2.5.1. Markov processes.- 2.5.2. Operators.- 2.5.3. Diffusion processes.- 2.5.4. Hypermixing.- 2.5.5. Hypercontractivity.- 2.5.6. Ultracontractivity.- 2.5.7. General SDE.