Probability in Banach Spaces, 9

1. Front Matter

   Pages i-vii

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2. Random Series, Exponential Moments, and Martingales

   1. Front Matter

      Pages 1-1

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   2. Convergence A.S. of Rearranged Random Series in Banach Space and Associated Inequalities

      • Sergej Chobanyan

      Pages 3-29

   3. On the Rademacher Series

      • Paweł Hitczenko, Stanisław Kwapień

      Pages 31-36

   4. On Separability of Families of Reversed Submartingales

      • Goran Peškir

      Pages 37-54

   5. Sharp Exponential Inequalities for the Martingales in the 2-Smooth Banach Spaces and Applications to “Scalarizing” Decoupling

      • Iosif Pinelis

      Pages 55-70

3. Strong Limit Theorems

   1. Front Matter

      Pages 71-71

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   2. Random Fractals Generated by Oscillations of Processes with Stationary and Independent Increments

      • Paul Deheuvels, David M. Mason

      Pages 73-89

   3. Some Generalized Martingales Arising from the Strong Law of Large Numbers

      • Bernard Heinkel

      Pages 91-104

   4. Uniform Ergodic Theorems for Dynamical Systems Under VC Entropy Conditions

      • Goran Peškir, Joseph E. Yukich

      Pages 105-128

   5. GB and GC Sets in Ergodic Theory

      • Michel Weber

      Pages 129-151

4. Weak Convergence

   1. Front Matter

      Pages 153-153

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   2. On the Central Limit Theorem for Multiparameter Stochastic Processes

      • M. Bloznelis, V. Paulauskas

      Pages 155-172

   3. Une caractérisation des espaces de Fréchet nucléaires Processes

      • X. Fernique

      Pages 173-181

   4. A Weighted Central Limit Theorem for a Function-Indexed Sum with Random Point Masses

      • Jens Præstgaard

      Pages 183-191

   5. On the Rate of Convergence in the CLT with Respect to the Kantorovich Metric

      • S. T. Rachev, L. Rüschendorf

      Pages 193-207

   6. Burgers’ Topology on Random Point Measures

      • Donatas Surgailis, Wojbor A. Woyczynski

      Pages 209-221

   7. On the Topological Description of Characteristic Functionals in Infinite Dimensional Spaces

      • Vazha I. Tarieladze

      Pages 223-238

5. Large Deviations and Measure Inequalities

   1. Front Matter

      Pages 239-239

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   2. Projective Systems in Large Deviation Theory II: Some Applications

      • A. de Acosta

      Pages 241-250

The papers contained in this volume are an indication of the topics th discussed and the interests of the participants of The 9 International Conference on Probability in Banach Spaces, held at Sandjberg, Denmark, August 16-21, 1993. A glance at the table of contents indicates the broad range of topics covered at this conference. What defines research in this field is not so much the topics considered but the generality of the ques­ tions that are asked. The goal is to examine the behavior of large classes of stochastic processes and to describe it in terms of a few simple prop­ erties that the processes share. The reward of research like this is that occasionally one can gain deep insight, even about familiar processes, by stripping away details, that in hindsight turn out to be extraneous. A good understanding about the disciplines involved in this field can be obtained from the recent book, Probability in Banach Spaces, Springer-Verlag, by M. Ledoux and M. Thlagrand. On page 5, of this book, there is a list of previous conferences in probability in Banach spaces, including the other eight international conferences. One can see that research in this field over the last twenty years has contributed significantly to knowledge in probability and has had important applications in many other branches of mathematics, most notably in statistics and functional analysis.

• Ergodic theory
• Estimator
• Gaussian measure
• Law of large numbers
• Likelihood
• Martingale
• Median
• Random variable
• Stochastic processes
• functional analysis
• statistics
• stochastic process

• Mathematical Institute, Aarhus University, Aarhus C, Denmark

  Jørgen Hoffmann-Jørgensen

• Department of Mathematics, University of Wisconsin, Madison, USA

  James Kuelbs

• Department of Mathematics, City College of New York, New York, USA

  Michael B. Marcus

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