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Weak convergence of stochastic processes is one of most important theories in probability theory. Not only probability experts but also more and more statisticians are interested in it. In the study of statistics and econometrics, some problems cannot be solved by the classical method. In this book, we will introduce some recent development of modern weak convergence theory to overcome defects of classical theory.boldContents:/boldbulletlistbulletboldThe Definition and Basic Properties of Weak Convergence:/bold/bulletbulletlistbulletMetric Space/bulletbulletThe Definition of Weak Convergence of Stochastic Processes and Portmanteau Theorem/bulletbulletHow to Verify the Weak Convergence?/bulletbulletTwo Examples of Applications of Weak Convergence/bullet/bulletlist/bulletbulletboldConvergence to the Independent Increment Processes:/bold/bulletbulletlistbulletThe Basic Conditions of Convergence to the Gaussian Independent Increment Processes/bulletbulletDonsker Invariance Principle/bulletbulletConvergence of Poisson Point Processes/bulletbulletTwo Examples of Applications of Point Process Method/bullet/bulletlist/bulletbulletboldConvergence to Semimartingales:/bold/bulletbulletlistbulletThe Conditions of Tightness for Semimartingale Sequence/bulletbulletWeak Convergence to Semimartingale/bulletbulletWeak Convergence to Stochastic Integral I: The Martingale Convergence Approach/bulletbulletWeak Convergence to Stochastic Integral II: Kurtz and Protter's Approach/bulletbulletStable Central Limit Theorem for Semimartingales/bulletbulletAn Application to Stochastic Differential Equations/bulletbulletAppendix: The Predictable Characteristics of Semimartingales/bullet/bulletlist/bulletbulletboldConvergence of Empirical Processes:/bold/bulletbulletlistbulletClassical Weak Convergence of Empirical Processes/bulletbulletWeak Convergence of Marked Empirical Processes/bulletbulletWeak Convergence of Function Index Empirical Processes/bulletbulletWeak Convergence of Empirical Processes Involving Time-Dependent data/bulletbulletTwo Examples of Applications in Statistics/bullet/bulletlist/bullet/bulletlistbr/boldReadership:/bold Graduate students and researchers in probability & statistics and econometrics.br/