Stable Convergence and Stable Limit Theorems
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
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Erich Häusler Harald Luschgy
Stable Convergence and Stable Limit Theorems
Probability Theory and Stochastic Modelling Volume 74
Editors-in-chief Søren Asmussen, Aarhus, Denmark Peter W. Glynn, Stanford, CA, USA Thomas G. Kurtz, Madison, WI, USA Yves Le Jan, Orsay, France Advisory Board Joe Gani, Canberra, ACT, Australia Martin Hairer, Coventry, UK Peter Jagers, Gothenburg, Sweden Ioannis Karatzas, New York, NY, USA Frank P. Kelly, Cambridge, UK Andreas E. Kyprianou, Bath, UK Bernt Øksendal, Oslo, Norway George Papanicolaou, Stanford, CA, USA Etienne Pardoux, Marseille, France Edwin Perkins, Vancouver, BC, Canada Halil Mete Soner, Zürich, Switzerland
The Probability Theory and Stochastic Modelling series is a merger and continuation of Springer’s two well established series Stochastic Modelling and Applied Probability and Probability and Its Applications series. It publishes research monographs that make a significant contribution to probability theory or an applications domain in which advanced probability methods are fundamental. Books in this series are expected to follow rigorous mathematical standards, while also displaying the expository quality necessary to make them useful and accessible to advanced students as well as researchers. The series covers all aspects of modern probability theory including • • • • • •
Gaussian processes Markov processes Random fields, point processes and random sets Random matrices Statistical mechanics and random media Stochastic analysis
as well as applications that include (but are not restricted to): • Branching processes and other models of population growth • Communications and processing networks • Computational methods in probability and stochastic processes, including simulation • Genetics and other stochastic models in biology and the life sciences • Information theory, signal processing, and image synthesis • Mathematical economics and finance • Statistical methods (e.g. empirical processes, MCMC) • Statistics for stochastic processes • Stochastic control • Stochastic models in operations research and stochastic optimization • Stochastic models in the physical sciences
More information about this series at http://www.springer.com/series/13205
Erich Häusler Harald Luschgy •
Stable Convergence and Stable Limit Theorems
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Erich Häusler Mathematical Institute University of Giessen Giessen Germany
Harald Luschgy FB IV, Mathematics University of Trier Trier Germany
ISSN 2199-3130 ISSN 2199-3149 (electronic) Probability Theory and Stochastic Modelling ISBN 978-3-319-18328-2 ISBN 978-3-319-18329-9 (eBook) DOI 10.1007/978-3-319-18329-9 Library of Congress Control Number: 2015938430 Mathematics Subject Classification (2010): 60-02, 60F05, 60F17 Springer Cham Heidelberg New York Dordrecht London © Springer International Publishing Switzerland 2015 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, bro
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