Probability in Banach Spaces, 8: Proceedings of the Eighth International Conference

1. Front Matter

   Pages I-XI

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2. Matching Theorems

   1. Front Matter

      Pages 1-1

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   2. An Exposition of Talagrand’s Mini-Course on Matching Theorems

      • Marjorie G. Hahn, Yongzhao Shao

      Pages 3-38

   3. The Ajtai-Komlos-Tusnady Matching Theorem for General Measures

      • Michel Talagrand

      Pages 39-54

   4. Some Generalizations of the Euclidean Two-Sample Matching Problem

      • J. Yukich

      Pages 55-66

3. Inequalities and Approximations

   1. Front Matter

      Pages 67-67

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   2. Sharp Bounds on the LP Norm of a Randomly Stopped Multilinear form with an Application to Wald’s Equation

      • Victor H. de la Peña

      Pages 69-79

   3. On Hoffmann-Jørgensen’s Inequality for U-Processes

      • Evarist Giné, Joel Zinn

      Pages 80-91

   4. The Poisson Counting Argument: A Heuristic for Understanding What Makes a Poissonized Sum Large

      • Marjorie G. Hahn, Michael J. Klass

      Pages 92-105

   5. On the Lower Tail of Gaussian Measures on l _p

      • Wenbo V. Li

      Pages 106-115

   6. Conditional Versions of the Strassen-Dudley Theorem

      • Ditlev Monrad, Walter Philipp

      Pages 116-127

   7. An Approach to Inequalities for the Distributions of Infinite-Dimensional Martingales

      • Iosif Pinelis

      Pages 128-134

4. Stochastic Processes

   1. Front Matter

      Pages 135-135

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   2. Random Integral Representations for Classes of Limit Distributions Similar to Levy Class L ₀. III

      • Zbigniew J. Jurek

      Pages 137-151

   3. Asymptotic Dependence of Stable Self-Similar Processes of Chentsov Type

      • Piotr S. Kokoszka, Murad S. Taqqu

      Pages 152-165

   4. Distributions of Stable Processes on Spaces of Measurable Functions

      • Rimas Norvaiša

      Pages 166-188

   5. Harmonizability, V-Boundedness, and Stationary Dilation of Banach-Valued Processes

      • Philip H. Richard

      Pages 189-205

5. Weak Convergence and Large Deviations

   1. Front Matter

      Pages 207-207

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   2. Asymptotic Behavior of Self-Normalized Trimmed Sums: Nonnormal Limits III

      • Marjorie G. Hahn, Daniel C. Weiner

      Pages 209-227

   3. On Large Deviations of Gaussian Measures in Banach Spaces

      • Marek Slaby

      Pages 228-244

Probability limit theorems in infinite-dimensional spaces give conditions un­ der which convergence holds uniformly over an infinite class of sets or functions. Early results in this direction were the Glivenko-Cantelli, Kolmogorov-Smirnov and Donsker theorems for empirical distribution functions. Already in these cases there is convergence in Banach spaces that are not only infinite-dimensional but nonsep­ arable. But the theory in such spaces developed slowly until the late 1970's. Meanwhile, work on probability in separable Banach spaces, in relation with the geometry of those spaces, began in the 1950's and developed strongly in the 1960's and 70's. We have in mind here also work on sample continuity and boundedness of Gaussian processes and random methods in harmonic analysis. By the mid-70's a substantial theory was in place, including sharp infinite-dimensional limit theorems under either metric entropy or geometric conditions. Then, modern empirical process theory began to develop, where the collection of half-lines in the line has been replaced by much more general collections of sets in and functions on multidimensional spaces. Many of the main ideas from probability in separable Banach spaces turned out to have one or more useful analogues for empirical processes. Tightness became "asymptotic equicontinuity. " Metric entropy remained useful but also was adapted to metric entropy with bracketing, random entropies, and Kolchinskii-Pollard entropy. Even norms themselves were in some situations replaced by measurable majorants, to which the well-developed separable theory then carried over straightforwardly.

• Brownian motion
• Gaussian measure
• Gaussian process
• Markov process
• Martingale
• Random variable
• distribution
• local time
• random walk
• self-similar process
• statistics

• Dept. of Mathematics, MIT, Cambridge, USA

  Richard M. Dudley

• Department of Mathematics, Tufts University, Medford, USA

  Marjorie G. Hahn

• Dept. of Mathematics, University of Wisconsin, Madison, USA

  James Kuelbs

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