Stochastic Inequalities and Applications
Concentration inequalities, which express the fact that certain complicated random variables are almost constant, have proven of utmost importance in many areas of probability and statistics. This volume contains refined versions of these inequalities, an
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Series Editors Thomas Liggett Charles Newman Loren Pitt Sidney 1. Resnick
Stochastic Inequalities and Applications Evariste Gine Christian Houdre David Nualart Editors
Springer Basel AG
Editors. addresses: Evariste Gine Department of Mathematics, U-3009 University of Connecticut Storrs, CT 06268 USA [email protected]
Christian Houdre Laboratoire d'Analyse et de Mathematiques Appliquees CNRS UMR 8050 Universite de Paris XII 94010 Creteil Cedex, France
David Nualart Universitat de Barcelona Facultat de Matematiques Gran Via, 585 08007 Barcelona Spain [email protected]
and School of Mathematics Georgia Institute ofTechnology Atlanta, GA 30332 USA [email protected]
2000 Mathematics Subject Classification 28CIO, 35B65, 37A50, 37H15, 44A60, 46B09, 49R50, 58C35, 58J65, 60Bl1, 60B99, 60El5, 60F05, 60F07, 60FlO, 60F99, 60Gxx, 60Hxx, 62BlO' 62El7, 62E20, 62F12, 62G30, 65M12, 65M15, 93D20, 93Ell, 94A17
A CIP catalogue record for this book is available from the Library of Congress, Washington D.C., USA
Bibliographic information published by Die Deutsche Bibliothek Die Deutsche Bibliothek lists this publication in the Deutsche Nationalbibliografie; detailed bibliographic data is available in the Internet at .
ISBN 978-3-0348-9428-9 ISBN 978-3-0348-8069-5 (eBook) DOI 10.1007/978-3-0348-8069-5 This work is subject to copyright. AlI rights are reserved, whether the whole or part of the material is concerned, specificalIy the rights of translation, reprinting, re-use of illustrations, broadcasting, reproduction on microfilms or in other ways, and storage in data banks. For any kind of use permission of the copyright owner must be obtained. © 2003 Springer Basel AG Originally published by Birkhăuser Verlag Basel in 2003 Softcover reprint ofthe hardcover Ist edition 2003 Printed on acid-free paper produced from chlorine-free pulp. TCF
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Table of Contents Preface ......... .. . ..... ... . ... .. . ...... .... .. .. .. . ..... ............ ... ...
vii
I. Geometric Inequalities
Sergey G. Bobkov and Fedor L. Nazarov Large Deviations of Typical Linear Functionals on a Convex Body with Unconditional Basis ............................................
3
Christian Houdre and Nicolas Privault A Concentration Inequality on Riemannian Path Space
15
Ioannis Kontoyiannis and Ali Devin Sezer A Remark on Unified Error Exponents: Hypothesis Testing, Data Compression and Measure Concentration ................. . .....
23
Paul-Marie Samson Concentration Inequalities for Convex Functions on Product Spaces
33
II. Independent Random Vectors, Chaos, Martingales and Levy Processes
Christian Houdre and Patricia Reynaud-Bouret Exponential Inequalities, with Constants, for U-statistics of Order Two
55
Stanislaw Kwapien and Vaja Tarieladze On a.s. Unconditional Convergence of Random Series in Banach Spaces
71
Rafal Latala and Rafal Lochowski Moment and Tail Estimates for Multidimensional Chaoses Generated by Positive Random Variables with Logarithmically Concave Tails .. .
77
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