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Convergence of Stochastic Processes
David Pollard
Springer-Verlag
format: djvu
quality: very good
Contents:
Notation
CHAPTER I
Functionals on Stochastic Processes
1. Stochastic Processes as Random Functions
Notes
Problems
CHAPTER II
Uniform Convergence of Empirical Measures
1. Uniformity and Consistency
2. Direct Approximation
3. The Combinatorial Method
4. Classes of Sets with Polynomial Discrimination
5. Classes of Functions
6. Rates of Convergence
Notes
Problems
CHAPTER III
Convergence in Distribution in Euclidean Spaces
1. The Definition
2. The Continuous Mapping Theorem
3. Expectations of Smooth Functions
4. The Central Limit Theorem
5. Characteristic Functions
6. Quantile Transformations and Almost Sure Representations
Notes
Contents
CHAPTER IV
Convergence in Distribution in Metric Spaces
1. Measurability
2. The Continuous Mapping Theorem
3. Representation by Almost Surely Convergent Sequences
4. Coupling
5. Weakly Convergent Subsequences
Notes
Problems
64
64
66
71
76
81
85
86
CHAPTER V
The Uniform Metric on Spaces of Cadlag Functions
1. Approximation of Stochastic Processes
2. Empirical Processes
3. Existence of Brownian Bridge and Brownian Motion
4. Processes with Independent Increments
5. Infinite Time Scales
6. Functionals of Brownian Motion and Brownian Bridge
Notes
Problems
CHAPTER VI
The Skorohod Metric on D[0,
1. Properties of the Metric
2. Convergence in Distribution
Notes
Problems
CHAPTER VII
Central Limit Theorems
1. Stochastic Equicontinuity
2. Chaining
3. Gaussian Processes
4. Random Covering Numbers
5. Empirical Central Limit Theorems
6. Restricted Chaining
Notes
Problems
CHAPTER VIII
Martingales
1. A Central Limit Theorem for Martingale-Difference Arrays
2. Continuous Time Martingales
3. Estimation from Censored Data
Notes
Problems
Contents
xi
APPENDIX A
Stochastic-Order Symbols
APPENDIX B
Exponential Inequalities
Notes
Problems
APPENDIX C
Measurability
Notes
Problems
References
Author Index
Subject Index
regards,
arunmit168.
David Pollard
Springer-Verlag
format: djvu
quality: very good
Contents:
Notation
CHAPTER I
Functionals on Stochastic Processes
1. Stochastic Processes as Random Functions
Notes
Problems
CHAPTER II
Uniform Convergence of Empirical Measures
1. Uniformity and Consistency
2. Direct Approximation
3. The Combinatorial Method
4. Classes of Sets with Polynomial Discrimination
5. Classes of Functions
6. Rates of Convergence
Notes
Problems
CHAPTER III
Convergence in Distribution in Euclidean Spaces
1. The Definition
2. The Continuous Mapping Theorem
3. Expectations of Smooth Functions
4. The Central Limit Theorem
5. Characteristic Functions
6. Quantile Transformations and Almost Sure Representations
Notes
Contents
CHAPTER IV
Convergence in Distribution in Metric Spaces
1. Measurability
2. The Continuous Mapping Theorem
3. Representation by Almost Surely Convergent Sequences
4. Coupling
5. Weakly Convergent Subsequences
Notes
Problems
64
64
66
71
76
81
85
86
CHAPTER V
The Uniform Metric on Spaces of Cadlag Functions
1. Approximation of Stochastic Processes
2. Empirical Processes
3. Existence of Brownian Bridge and Brownian Motion
4. Processes with Independent Increments
5. Infinite Time Scales
6. Functionals of Brownian Motion and Brownian Bridge
Notes
Problems
CHAPTER VI
The Skorohod Metric on D[0,
1. Properties of the Metric
2. Convergence in Distribution
Notes
Problems
CHAPTER VII
Central Limit Theorems
1. Stochastic Equicontinuity
2. Chaining
3. Gaussian Processes
4. Random Covering Numbers
5. Empirical Central Limit Theorems
6. Restricted Chaining
Notes
Problems
CHAPTER VIII
Martingales
1. A Central Limit Theorem for Martingale-Difference Arrays
2. Continuous Time Martingales
3. Estimation from Censored Data
Notes
Problems
Contents
xi
APPENDIX A
Stochastic-Order Symbols
APPENDIX B
Exponential Inequalities
Notes
Problems
APPENDIX C
Measurability
Notes
Problems
References
Author Index
Subject Index
regards,
arunmit168.
