Author | Pollard, David. author |
---|---|
Title | Convergence of Stochastic Processes [electronic resource] / by David Pollard |
Imprint | New York, NY : Springer New York, 1984 |
Connect to | http://dx.doi.org/10.1007/978-1-4612-5254-2 |
Descript | 215 p. online resource |
I Functional on Stochastic Processes -- 1. Stochastic Processes as Random Functions -- 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 -- 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 -- 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 -- 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. Functional of Brownian Motion and Brownian Bridge -- VI The Skorohod Metric on D(0, ?) -- 1. Properties of the Metric -- 2. Convergence in Distribution -- VII Central Limit Theorems -- 1. Stochastic Equicontinuity -- 2. Chaining -- 3. Gaussian Processes -- 4. Random Covering Numbers -- 5. Empirical Central Limit Theorems -- 6. Restricted Chaining -- VIII Martingales -- 1. A Central Limit Theorem for Martingale-Difference Arrays -- 2. Continuous Time Martingales -- 3. Estimation from Censored Data -- Appendix A Stochastic-Order Symbols -- Appendix B Exponential Inequalities -- Notes -- Problems -- Appendix C Measurability -- Notes -- Problems -- References -- Author Index