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. Language: English