The authors present a concise but complete exposition of the mathematical theory of stable convergence and give various applications in different areas of probability theory and mathematical statistics to illustrate the usefulness of this concept. Stable convergence holds in many limit theorems of probability theory and statistics – such as the classical central limit theorem – which are us…
Weak convergence of probability measures or, what is the same, convergence in distribution of random variables is arguably one of the most important basic concepts of asymptotic probability theory and mathematical statistics. The classical central limit theorem for sums of independent real random variables, a cornerstone of these fields, cannot possibly be thought of properly without the not…