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Wahrscheinlichkeitstheorie gehort zu den Grundveranstaltungen fast aller Studiengange. Dieses Lehrburch fuhrt schnell, verlasslich und prazise zu den wichtigsten Ergebnissen der Wahrscheinlichkeitstheorie hin.

Brownsche Bewegungen sind eine der wichtigsten stochastischen Prozesse in stetiger Zeit mit stetigem Phasenraum. Dieses Lehrburch fuhrt schnell, verlasslich und prazise zu den wichtigsten Ergebnissen der Theorie der Brownschen Bewegungen hin.

Allgemeine Mae und das Lebesgue-Integral gehoren zu den unverzichtbaren Hilfsmitteln der modernen Analysis, der Funktionalanalysis und der Stochastik. Das vorliegende Lehrbuch bietet eine Einfuhrung in die wesentlichen Aspekte der Theorie - Mae, Integrale, Konvergenzsatze, Parameterintegrale, Satz von Fubini -, die durch weiterfuhrende Themen - allgemeiner Transformationssatz, Satz von Radon-Nikodym, Fouriertransformation von Maen, topologische Matheorie - abgerundet wird. Mehr als 150 Ubungsaufgaben (mit vollstandigen Losungen im Internet) vertiefen und erweitern den Stoff.

Die...

This extensive selection of William Feller's scientific papers shows the breadth of his oeuvre as well as the historical development of his scientific interests. Six seminal papers - originally written in German - on the central limit theorem, the law of large numbers, the foundations of probability theory, stochastic processes and mathematical biology are now, for the first time, available in English. The material is accompanied by detailed scholarly comments on Feller's work and its impact, a complete bibliography, a list of his PhD students as well as a biographic sketch of his life...

This extensive selection of William Feller's scientific papers shows the breadth of his oeuvre as well as the historical development of his scientific interests. Six seminal papers - originally written in German - on the central limit theorem, the law of large numbers, the foundations of probability theory, stochastic processes and mathematical biology are now, for the first time, available in English. The material is accompanied by detailed scholarly comments on Feller's work and its impact, a complete bibliography, a list of his PhD students as well as a biographic sketch of his life...

Bernstein functions appear in various fields of mathematics, e.g. probability theory, potential theory, operator theory, functional analysis and complex analysis - often with different definitions and under different names. Among the synonyms are Laplace exponent' instead of Bernstein function, and complete Bernstein functions are sometimes called Pick functions', Nevanlinna functions' or operator monotone functions'.

This monograph - now in its second revised and extended edition - offers a self-contained and unified approach to Bernstein functions and closely related function...