Weak Convergence and the Poisson Process
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This chapter exploits connections between regular variation and the Poisson process given in Theorems 6.2 (p. 179) and 6.3 (p. 180) to understand several limit theorems and also to understand how regular variation of distributions of random vectors is transmitted by various transformations on the vectors. The fundamental philosophy is that we should capitalize on the equivalence between the analytical concept of regular variation and the probabilistic notion of convergence of empirical measures to limiting Poisson random measures.
KeywordsRandom Vector Weak Convergence Regular Variation Nonnegative Random Variable Extremal Process
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