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 usually formulated in terms of convergence in distribution.
Originated by Alfred Rényi the notion of stable convergence is stronger than the classical
weak convergence of probability measures. A variety of methods is described which can be used
to establish this stronger stable convergence in many limit theorems which were originally
formulated only in terms of weak convergence. Naturally these stronger limit theorems have new
and stronger consequences which should not be missed by neglecting the notion of stable
convergence. The presentation will be accessible to researchers and advanced students at the
master's level with a solid knowledge of measure theoretic probability.
