Probability in Banach Spaces, 9: (35 Progress in Probability)

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.

Table of Contents:
Random Series, Exponential Moments, and Martingales.- Convergence a.s. of rearranged random series in Banach space and associated inequalities.- On the Rademacher series.- On separability of families of reversed submartingales.- Sharp exponential inequalities for the Martingales in the 2-smooth Banach spaces and applications to “scalarizing” decoupling.- Strong Limit Theorems.- Random fractals generated by oscillations of processes with stationary and independent increments.- Some generalized Martingales arising from the strong law of large numbers.- Uniform ergodic theorems for dynamical systems under VC entropy conditions.- GB and GC sets in ergodic theory.- Weak Convergence.- On the central limit theorem for multiparameter stochastic processes.- Une caractérisation des espaces de Fréchet nucléaires.- A weighted central limit theorem for a function-indexed sum with random point masses.- On the rate of convergence in the CLT with respect to the Kantorovich metric.- Burgers’ topology on random point measures.- On the topological description of characteristic functionals in infinite dimensional spaces.- Large Deviations and Measure Inequalities.- Projective systems in large deviation theory II: some applications.- Some large deviation results for Gaussian measures.- A remark on the median and the expectation of convex functions of Gaussian vectors.- Comparison results for the small ball behavior of Gaussian random variables.- Some remarks on the Berg-Kesten inequality.- Gaussian Chaos and Wiener Measures.- On Girsanov type theorem for anticipative shifts.- A necessary condition for the continuity of linear functionals of Wick squares.- Multiple Wiener-Itô integral processes with sample paths in Banach function spaces.- A remark on Sudakov minoration for chaos.-Topics in Empirical Processes, Spacing Estimates, and Applications to Maximum Likelihood Theory.- On the weak Bahadur-Kiefer representation for M-estimators.- Stochastic differentiability in maximum likelihood theory.- A uniform law of large numbers for set-indexed processes with applications to empirical and partial-sum processes.- Bahadur-Kiefer approximation for spatial quantiles.- Maximum spacing estimates: a generalization and improvement on maximum likelihood estimates I.