Weak Convergence
Harold J. Kushner · Birkhäuser Boston eBooks · 1990
The basic questions dealt with in this book concern approximations of relatively complex processes by simpler and more tractable processes. These processes might be controlled or not controlled. The approximation might be of interest for either the purposes of engineering design, or for other analytical or numerical work. The theory of weak convergence of measures seems to be the fundamental and most widely used and successful tool for such purposes. See, for example, the techniques, examples and references in the books [B6, E2, K20]. In this chapter, we will discuss the basic ideas in the subject which will be useful for our work in the sequel. The detailed examples will not be dealt with in this chapter, but are left to the rest of the book. The basic techniques discussed in this chapter will all be further developed and worked out in detail in connection with the applications dealt with in the succeeding chapters. The concepts and criteria have a rather abstract flavor as they are initially introduced, but when applied in the succeeding chapters, they take on concrete and readily usable forms.