Weak Convergence And Its Applications

by Zhengyan Lin, Hanchao Wang

Overview

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.

Product Details

ISBN-13:	9789814447690
Publisher:	World Scientific Publishing Company, Incorporated
Publication date:	07/07/2014
Pages:	184
Product dimensions:	6.70(w) x 9.80(h) x 0.70(d)

Table of 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; Convergence of Empirical Processes:; Classical Weak Convergence of Empirical Processes; Weak Convergence of Marked Empirical Processes; Weak Convergence of Function Index Empirical Processes; Weak Convergence of Empirical Processes Involving Time-Dependent data; Two Examples of Applications in Statistics;