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eISBN : 9780511320798

Contents : Contents
Preface
Acknowledgment
Notation
1 Dynamical Systems
1.1 Introduction
1.2 Basic Definitions: Fixed and Periodic Points
1.3 Complexity
1.3.1 Li–Yorke Chaos and Sarkovskii Theorem
1.3.2 A Remark on Robustness of Li–Yorke Complexity
1.3.3 Complexity: Alternative Approaches
1.4 Linear Difference Equations
1.5 Laws of Motion
1.6 Thresholds and Critical Stocks
1.7 The Quadratic Family
1.7.1 Stable Periodic Orbits
1.8 Comparative Statics and Dynamics
1.8.1 Bifurcation Theory
1.9 Some Applications
1.9.1 The Harrod–Domar Model
1.9.2 The Solow Model
1.9.3 Balanced Growth and Multiplicative Processes
1.9.4 Models of Intertemporal Optimization with a Single Decision Maker
1.9.5 Optimization with Wealth Effects: Periodicity and Chaos
1.9.6 Dynamic Programming
1.9.7 Dynamic Games
1.9.8 Intertemporal Equilibrium
1.9.9 Chaos in Cobb–Douglas Economies
1.10 Complements and Details
1.11 Supplementary Exercises
2 Markov Processes
2.1 Introduction
2.2 Construction of Stochastic Processes
2.3 Markov Processes with a Countable Number States
2.4 Essential, Inessential, and Periodic States of a Markov Chain
2.5 Convergence to Steady States for Markov Processes on Finite State Spaces
2.6 Stopping Times and the Strong Markov Property of Markov Chains
2.7 Transient and Recurrent Chains
2.8 Positive Recurrence and Steady State Distributions of Markov Chains
2.9 Markov Processes on Measurable State Spaces: Existence of and Convergence to Unique Steady States
2.10 Strong Law of Large Numbers and Central Limit Theorem
2.11 Markov Processes on Metric Spaces: Existence of Steady States
2.12 Asymptotic Stationarity
2.13 Complements and Details
2.13.1 Irreducibility and Harris Recurrent Markov Processes
2.14 Supplementary Exercises
3 Random Dynamical Systems
3.1 Introduction
3.2 Random Dynamical Systems
3.3 Evolution
3.4 The Role of Uncertainty: Two Examples
3.5 Splitting
3.5.1 Splitting and Monotone Maps
3.5.2 Splitting: A Generalization
3.5.3 The Doeblin Minorization Theorem Once Again
3.6 Applications
3.6.1 First-Order Nonlinear Autoregressive Processes (NLAR(1))
3.6.2 Stability of Invariant Distributions in Models of Economic Growth
3.6.3 Interaction of Growth and Cycles
3.6.4 Comparative Dynamics
3.7 Contractions
3.7.1 Iteration of Random Lipschitz Maps
3.7.2 Variant Due to Dubins and Freedman
3.8 Complements and Details
3.9 Supplementary Exercises
4 Random Dynamical Systems: Special Structures
4.1 Introduction
4.2 Iterates of Real-Valued Affine Maps (AR(1) Models)
4.3 Linear Autoregressive (LAR(k)) and Other Linear Time Series Models
4.4 Iterates of Quadratic Maps
4.5 NLAR (k) and NLARCH (k) Models
4.6 Random Continued Fractions
4.6.1 Continued Fractions: Euclid's Algorithm and the Dynamical System of Gauss
4.6.2 General Continued Fractions and Random Continued Fractions
4.6.3 Bernoulli Innovation
4.7 Nonnegativity Constraints
4.8 A Model with Multiplicative Shocks, and the Survival Probability of an Economic Agent
4.9 Complements and Details
5 Invariant Distributions: Estimation and Computation
5.1 Introduction
5.2 Estimating the Invariant Distribution
5.3 A Sufficient Condition for vn-Consistency
5.3.1 vn-Consistency
5.4 Central Limit Theorems
5.5 The Nature of the Invariant Distribution
5.5.1 Random Iterations of Two Quadratic Maps
5.6 Complements and Details
5.7 Supplementary Exercises
6 Discounted Dynamic Programming Under Uncertainty
6.1 Introduction
6.2 The Model
6.2.1 Optimality and the Functional Equation of Dynamic Programming
6.3 The Maximum Theorem: A Digression
6.3.1 Continuous Correspondences
6.3.2 The Maximum Theorem and the Existence of a Measurable Selection
6.4 Dynamic Programming with a Compact Action Space
6.5 Applications
6.5.1 The Aggregative Model of Optimal Growth Under Uncertainty: The Discounted Case
6.5.2 Interior Optimal Processes
6.5.3 The Random Dynamical System of Optimal Inputs
6.5.4 Accumulation of Risky Capital
6.6 Complements and Details
6.6.1 Upper Semicontinuous Model
6.6.2 The Controlled Semi-Markov Model
6.6.3 State-Dependent Actions
A Appendix
A1. Metric Spaces: Separability, Completeness, and Compactness
A1.1. Separability
A1.2. Completeness
A1.3. Compactness
A2. Infinite Products of Metric Spaces and the Diagonalization Argument
A3. Measurability
A3.1. Subspaces
A3.2. Product Spaces: Separability Once Again
A3.3. The Support of a Measure
A3.4. Change of Variable
A4. Borel-Cantelli Lemma
A5. Convergence
Bibliography
Author Index
Subject Index

Language : English

Place of publishing : CAMBRIDGE

Location : Nice Library

Material : Electronic

Statement : Présent

Owner : Bibliothèque