Weak convergence and its application (Q2838246)

This well-written book is intended as a systematic exposition of the theory of weak convergence of probability measures on metric spaces, covering a wide range of weak convergence problems including new developments. The chapter headings are: 1. The definition and basic properties of weak convergence, 2. Convergence to independent increment processes, 3. Convergence to semimartingales, 4. Convergence of empirical processes. NEWLINENEWLINENEWLINEIn Chapter 1, the authors present some definition and properties of weak convergence, including the portmanteau theorem of weak convergence and some important examples. Chapter 2 deals with weak convergence to independent increment processes. The following aspects are considered: Donsker type invariance principles, i.e., weak convergence to Gaussian independendent increment processes, and point process convergence, i.e., weak convergence to compound Poisson type processes. Chapter 3 on weak convergence to semimartingales covers the general case of convergence to semimartingales and, as example, weak convergence to stochastics integrals. In Chapter 4, the classical weak convergence results of empirical processes, the convergence of function indexed empirical processes and some applications are presented.NEWLINENEWLINEIn summary, the book is a solid mathematical treatment of some topics in the modern theory of weak convergence. In addition, it is a useful guide to some recent applications of weak convergence theory in time series, statistics and econometrics. Some of the results belong to the authors.