Click Here to Download: https://ouo.io/y73QOk Weak Convergence And Its Applications By: Zhengyan Lin; Hanchao Wang Publisher: WSPC Print ISBN: 9789814447690, 9814447692 eText ISBN: 9789814447713, 9814447714 Pages: 184 Format: EPUB Available from $ 38.00 USD SKU 9789814447713 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. Contents: The Definition and Basic Properties of Weak Convergence: Metric Space The Definition of Weak Convergence of Stochastic Processes and Portmanteau Theorem How to Verify the Weak Convergence? Two Examples of Applications of Weak Convergence Convergence to the Independent Increment Processes: The Basic Conditions of Convergence to the Gaussian Independent Increment Processes Donsker Invariance Principle Convergence of Poisson Point Processes Two Examples of Applications of Point Process Method Convergence to Semimartingales: The Conditions of Tightness for Semimartingale Sequence Weak Convergence to Semimartingale Weak Convergence to Stochastic Integral I: The Martingale Convergence Approach Weak Convergence to Stochastic Integral II: Kurtz and Protter's Approach Stable Central Limit Theorem for Semimartingales An Application to Stochastic Differential Equations Appendix: The Predictable Characteristics of Semimartingales Graduate students and researchers in probability & statistics and econometrics.
