لایب سان

Ebook details:
عنوان: Nonconventional Limit Theorems and Random Dynamics
نویسنده: Yuri Kifer, Yeor Hafouta
ناشر: World Scientific Publishing Company (April 5, 2018)
زبان: English
شابک: 9813235004, 978-9813235007
حجم: 3 Mb
فرمت: True Pdf

Intro; Contents; Preface; Nonconventional Limit Theorems; 1. Stein's method in the nonconventional setup; 1.1 Introduction: local (strong) dependence structure; 1.2 Stein's method for normal aproximation; 1.2.1 A short introduction; 1.2.2 Normal approximation for graphical indexation; 1.2.3 Weak local dependence coefficients; 1.2.4 Relations with more familiar mixing coefficients; 1.3 Nonconventional CLT with convergence rates; 1.3.1 Assumptions and main results; 1.3.2 Asymptotic variance; 1.3.3 CLT with convergence rate; 1.3.4 The associated strong dependency graphs 1.3.5 Expectation estimates1.3.6 Proof of Theorem 1.3.7; 1.3.7 Back to graphical indexation; 1.4 General Stein's estimates: proofs; 1.4.1 Proof of Theorem 1.2.1; 1.4.2 Proof of Theorem 1.2.2; 1.5 Stein's method for diffusion approximations; 1.5.1 A functional CLT via Stein's method; 1.5.2 Finite dimensional convergence rate; 1.6 A nonconventional functional CLT; 1.7 Extensions to nonlinear indexes; 1.7.1 Preliminaries; 1.7.2 Another example with nonlinear indexes; 2. Local limit theorem; 2.1 Introduction; 2.2 Local central limit theorem via Fourier analysis 2.3 Nonconventional LLT for Markov chains by reduction to random dynamics2.4 Markov chains with densities; 2.4.1 Basic assumptions and CLT; 2.4.2 Characteristic functions estimates; 2.5 Markov chains related to dynamical systems; 2.5.1 Locally distance expanding maps and transfer operators; 2.5.2 Inverse branches, the pairing property and periodic points; 2.5.3 Thermodynamic formalism constructions and the associated Markov chains; 2.5.4 Relations between dynamical systems and Markov chains; 2.5.5 Mixing and approximation assumptions; 2.5.6 Asymptotic variance and the CLT 2.6 Statement of the local limit theorem2.7 The associated random transfer operators; 2.7.1 Random complex RPF theorem; 2.7.2 Distortion properties; 2.7.3 Reduction to random dynamics; 2.8 Decay of characteristic functions for small t's; 2.8.1 The random pressure function; 2.8.2 The derivatives of the pressure; 2.8.3 Pressure near 0; 2.8.4 Norms estimates: employing the pressure; 2.8.5 Remarks; 2.9 Decay of characteristic functions for large t's; 2.9.1 Basic estimates and strategy of the proof; 2.9.2 Probabilities of large number of visits to open sets; 2.9.3 Segments of periodic orbits 2.9.4 Parametric continuity of transfer operators2.9.5 Quasi compactness of Rit, lattice and non-lattice cases; 2.9.6 Norms estimates; 2.10 The periodic point approach to quenched and annealed dynamics; 2.11 Extensions to dynamical systems; 2.11.1 Subshifts of finite type; 2.11.2 The strategy of the proof; 2.11.3 Local limit theorem: one sided case; 2.11.4 Two sided case; 2.11.5 Reduction to one sided case; 3. Nonconventional arrays; 3.1 Introduction; 3.2 Strong law of large numbers for nonconventional arrays; 3.2.1 Setup and the main result; 3.2.2 Auxiliary lemmas

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