Probability in Banach Spaces

This volume includes a selection of papers by the participants of the Probability in Banach Spaces Conference held at Sanjberg, Denmark, August 16-21, 1993. The papers include recent advances in classical and modern limit theorems in Banach spaces as well as papers in which the techniques developed in this area are applied to empirical processes, spacing estimates, large deviation probabilities, measure inequalities and the study of stochastic processes. Researchers and advanced graduate students in probability, statistics, and functional analysis should find much of interest in both the theoretical concepts presented and their applications.

Table of Contents:
Part 1 Random series, exponential moments, and martingales: convergence a.s. of rearranged random series in Banach space and associated inequalities, Sergej Chobanyan; on the Rademacher series, Pawel Hitczenko and Stanislaw Kwapien; on separability of families of reversed submartingales, Goran Peskir; sharp exponential inequalities for the martingales in the 2-smooth Banach spaces and applications to "scalarizing" decoupling, Iosif Pinelis. Part 2 Strong limit theorems: random fractals generated by oscillations of processes with stationary and independent increments, Paul Deheuvels and David M. Mason; some generalized martingales arising from the strong law of large numbers, Bernard Heinkel; uniform ergodic theorems for dynamical systems under VC entropy conditions, Goran Peskir and Joseph E. Yukich; GB and GC sets in ergodic theory, Michel Weber. Part 3 Weak convergence: on the central limit theorem for multiparameter stochastic processes, M. Bloznelis and V. Paulauskas; une caracterisation des espaces de Frechet nucleaires, X. Fernique; a weighted central limit theorem for a function-indexed sum with random point masses, Jens Praestgaard; on the rate of convergence in the CLT with respect to the Kantorovich metric, S.T. Rachev and L. Ruschendorf; Burgers' topology on random point measures, Donatas Surgailis and Wojbor A. Woyczynski; on the topological description of characteristic functionals in infinite dimensional spaces, Vazha I. Tarieladze. Part 4 Large deviations and measure inequalities: projective systems in large deviation theory II - some applications, A. de Acosta; some large deviation results for Gaussian measures, J. Kuelbs and W.V. Li; a remark on the median and the expectation of convex functions of Gaussian vectors, Stanislaw Kwapien; comparison results for the small ball behaviour of Gaussian random variables, Werner Linde; some remarks on the Berg-Kesten inequality, Michel Talagrand. Part 5 Gaussian chaos and Wiener measures: on Girsanov type theorem for anticipative shifts, L. Gawarecki and V. Mandrekar; a necessary condition for the continuity of linear functionals of Wick squares, Michael B. Marcus; multiple Wiener-Ito integral processes with sample paths in Banach function spaces, Rimas Norvaisa; a remark on Sudakov minoration for chaos, Michel Talagrand. Part 6 Topics in empirical processes, spacing estimates, and applications to maximum likelihood theory: on the weak Bahadur-Kiefer representation for M-estimators, Miguel A. Arcones; stochastic differentiability in maximum likelihood theory, Vladimir Dobric and Cathy Liebars; a uniform law of large numbers for set-indexed processes with applications to empirical and partial-sum processes, Peter Gaenssler and Klaus Ziegler; Bahadur-Kiefer approximation for spatial quantiles, V. Koltchinskii; maximum spacing estimates - a generalization and improvement on maximum likelihood estimates I, Yongzhao Shao and Marjorie G. Hahn.