The series is devoted to the publication of monographs and high-level textbooks in mathematics, mathematical methods and their applications. Apart from covering important areas of current interest, a major aim is to make topics of an interdisciplinary nature accessible to the non-specialist. The works in this series are addressed to advanced students and researchers in mathematics and theoretical physics. In addition, it can serve as a guide for lectures and seminars on a graduate level. The series de Gruyter Studies in Mathematics was founded ca. 35 years ago by the late Professor Heinz Bauer and Professor Peter Gabriel with the aim to establish a series of monographs and textbooks of high standard, written by scholars with an international reputation presenting current fields of research in pure and applied mathematics. While the editorial board of the Studies has changed with the years, the aspirations of the Studies are unchanged. In times of rapid growth of mathematical knowledge carefully written monographs and textbooks written by experts are needed more than ever, not least to pave the way for the next generation of mathematicians. In this sense the editorial board and the publisher of the Studies are devoted to continue the Studies as a service to the mathematical community. Please submit any book proposals to Niels Jacob.

The fifth volume of Rudolf Ahlswede's lectures on Information Theory focuses on several problems that were at the heart of a lot of his research. One of the highlights of the entire lecture note series is surely Part I of this volume on arbitrarily varying channels (AVC), a subject in which Ahlswede was probably the world's leading expert. Appended to Part I is a survey by Holger Boche and Ahmed Mansour on recent results concerning AVC and arbitrarily varying wiretap channels (AVWC). After a short Part II on continuous data compression, Part III, the longest part of the book, is devoted to distributed information. This Part includes discussions on a variety of related topics; among them let us emphasize two which are famously associated with Ahlswede: "multiple descriptions", on which he produced some of the best research worldwide, and "network coding", which had Ahlswede among the authors of its pioneering paper. The final Part IV on "Statistical Inference under Communication constraints" is mainly based on Ahlswede's joint paper with Imre Csiszar, which received the Best Paper Award of the IEEE Information Theory Society. The lectures presented in this work, which consists of 10 volumes, are suitable for graduate students in Mathematics, and also for those working in Theoretical Computer Science, Physics, and Electrical Engineering with a background in basic Mathematics. The lectures can be used either as the basis for courses or to supplement them in many ways. Ph.D. students will also find research problems, often with conjectures, that offer potential subjects for a thesis. More advanced researchers may find questions which form the basis of entire research programs.

The purpose of the conference was to represent recent developments in measure theoretic, differentiable and topological dynamical systems as well as connections to probability theory, stochastic processes, operator theory and statistical physics. Only original research papers that do not appear elsewhere are included in the proceedings. Their topics include: C(2)-diffeomorphisms of compact Riemann manifolds, geodesic flows, chaotic behaviour in billards, nonlinear ergodic theory, central limit theorems for subadditive processes, Hausdorff measures for parabolic rational maps, Markov operators, periods of cycles, Julia sets, ergodic theorems. From the Contents: L.A. Bunimovich: On absolutely focusing mirrors.- M. Denker, M. Urbanski: The dichotomy of Hausdorff measures and equilibrium states for parabolic rational maps.- F. Ledrappier: Ergodic properties of the stable foliations.- U. Wacker: Invariance principles and central limit theorems for nonadditive stationary processes.- J. Schmeling, R. Siegmund-Schultze: Hoelder continuity of the holonomy map for hyperbolic basic sets.- A.M. Blokh: The spectral decomposition, periods of cycles and Misiurewicz conjecture for graph maps.- and contributions by Chr. Bandt and K. Keller, T. Bogenschutz andH. Crauel, H.G. Bothe, M. Denker and K.F. Kramer, T.P. Hill and U. Krengel, A. Iwanik, Z.S. Kowalski, E. Lesigne, J. Malczak, I. Mizera, J. Sipos, R. Wittmann.

Stochastik ist die Mathematik des Zufalls. Sie ist von grosster Bedeutung fur die Berufspraxis der Mathematiker. An vielen Schulen hat sie ihren festen Platz gefunden. Die beiden Hauptgebiete der Stochastik sind Wahrscheinlichkeitstheorie und Statistik.

in die Wahrscheinlichkeitstheorie und Statistik Friedr. Vieweg & Sohn Braunschweig I Wiesbaden Der Verlag Vieweg ist ein Unternehmen der Verlagsgruppe Bertelsmann. Alle Rechte vorbehalten (c) Friedr. Vieweg & Sohn Verlagsgesellschaft mbH, Braunschweig 1988 Das Werk einschliesslich aller seiner Teile ist urheberrechtlich geschutzt. Jede Verwertung ausserhalb der engen Grenzen des Urheberrechtsgesetzes ist ohne Zustimmung des Verlags unzulassig und stratbar. Das gilt insbesondere fur Vervielfaltigungen, UEbersetzungen, Mikroverfilmungen und die Einspeicherung und Verarbeitung in elektronischen Systemen. Satz: Vieweg, Braunschweig Buchbinderische Verarbeitung: W. Langeluddecke, Braunschweig ISBN 978-3-528-07259-9 ISBN 978-3-322-96418-2 (eBook) DOI 10.1007/978-3-322-96418-2 v Vorwort Dieses Buch entstand aus einem Skript fur eine in Goettingen regelmassig gehaltene vierstUEI1dige einfuhrende Vorlesung fur Mathematiker, Physiker und Lehramtskandidaten. Da das Skript auch an vielen anderen Universitaten Freunde gefunden hat, habe ich mich zur Publikation entschlossen. Stochastik ist die Mathematik des Zufalls. Sie ist von groesster Bedeutung fur die Berufspraxis der Mathematiker. An vielen Schulen hat sie ihren festen Platz gefunden. Die beiden Hauptgebiete der Stochastik sind Wahrscheinlichkeitstheorie und Statistik. In der Wahrscheinlichkeitstheorie untersucht man zufallige Prozesse mit festen als bekannt angenommenen steuernden Wahrscheinlichkeiten. Dies ist theoretisch und praktisch von eigenstandigem Interesse. Daruber hinaus liefert die Wahrscheinlichkeits- theorie Grundlagen fur die Statistik, in der aus beobachteten Daten Schlusse uber unbe- kannte Wahrscheinlichkeiten und uber zweckmassiges Verhalten gezogen werden sollen.