Preface
Contents
Symbol Definition List
1 Fourier Analysis: A Brief Survey
Exercises
2 Weakly Stationary Processes and Their Spectral Measures
Exercises
3 Spectral Representation of Stationary Processes
Exercises
4 Birkhoff's Ergodic Theorem
Exercises
5 Subadditive Ergodic Theory
Exercises
6 An Introduction to Dynamical Systems
Exercises
7 Markov Chains
Exercises
8 Markov Processes with General State Space
Exercises
9 Stopping Times and the Strong Markov Property
Exercises
10 Transience and Recurrence of Markov Chains
Exercises
11 BirthβDeath Chains
Exercises
12 Hitting Probabilities & Absorption
Exercises
13 Law of Large Numbers and Invariant Probability for Markov Chains by Renewal Decomposition
Exercises
14 The Central Limit Theorem for Markov Chains by Renewal Decomposition
Exercises
15 Martingale Central Limit Theorem
Exercises
16 Stationary Ergodic Markov Processes: SLLN & FCLT
Exercises
17 Linear Markov Processes
Exercises
18 Markov Processes Generated by Iterations of I.I.D. Maps
Exercises
19 A Splitting Condition and Geometric Rates of Convergence to Equilibrium
Exercises
20 Irreducibility and Harris Recurrent Markov Processes
Exercises
21 An Extended PerronβFrobenius Theorem and Large Deviation Theory for Markov Processes
Exercises
22 Special Topic: Applications of Large Deviation Theory
Exercises
23 Special Topic: Associated Random Fields, Positive Dependence, FKG Inequalities
Exercises
24 Special Topic: More on Coupling Methods and Applications
Exercises
25 Special Topic: An Introduction to Kalman Filter
Exercises
A Spectral Theorem for Compact Self-Adjoint Operators and Mercer's Theorem
B Spectral Theorem for Bounded Self-Adjoint Operators
C Borel Equivalence for Polish Spaces
D HahnβBanach, Separation, and Representation Theorems in Functional Analysis
References
Related Textbooks and Monographs
Author Index
Subject Index