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Martingale haben die Wahrscheinlichkeitstheorie derart revolutioniert, dass die Suche nach guten Martingalen inzwischen eine Standardmethode zur Untersuchung stochastischer Probleme ist. Das Buch fuhrt in die Theorie der reellen Martingale in diskreter Zeit ein und zeigt in Teil 2 einige ihrer Anwendungen; dazu zahlen u.a. das finanzmathematische Problem der Optionsbewertung, der Galton-Watson-Verzweigungsprozess, U-Statistiken und die unbedingte Basiseigenschaft von Martingal-Basen in Lp-Raumen. Mit zahlreichen Ubungsaufgaben zu jedem Kapitel."

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.

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.

Due to the rapidly increasing need for methods of data compression, quantization has become a flourishing field in signal and image processing and information theory. The same techniques are also used in statistics (cluster analysis), pattern recognition, and operations research (optimal location of service centers). The book gives the first mathematically rigorous account of the fundamental theory underlying these applications. The emphasis is on the asymptotics of quantization errors for absolutely continuous and special classes of singular probabilities (surface measures, self-similar...