Probability in Banach Spaces 7: Proceedings of the Seventh International Conference(21 Progress in Probability)

The first international conference on Probability in Banach Spaces was held at Oberwolfach, West Germany, in 1975. It brought together European researchers who, under the inspiration of the Schwartz Seminar in Paris, were using probabi­ listic methods in the study of the geometry of Banach spaces, a rather small number of probabilists who were already studying classical limit laws on Banach spaces, and a larger number of probabilists, specialists in various aspects of the study of Gaussian processes, whose results and techniques were of interest to the members of the first two groups. This first conference was very fruitful. It fos­ tered a continuing relationship among 50 to 75 probabilists and analysts working on probability on infinite-dimensional spaces, the geometry of Banach spaces, and the use of random methods in harmonic analysis. Six more international conferences were held since the 1975 meeting. Two of the meetings were held at Tufts University, one at S¢nderborg, Denmark, and the others at Oberwolfach. This volume contains a selection of papers by the partici­ pants of the Seventh International Conference held at Oberwolfach, West Ger­ many, June 26-July 2, 1988. This exciting and provocative conference was at­ tended by more than 50 mathematicians from many countries. These papers demonstrate the range of interests of the conference participants. In addition to the ongoing study of classical and modern limit theorems in Banach spaces, a branching out has occurred among the members of this group.

Table of Contents:
On the functional law of the iterated logarithm for recurrent events.- Sur la loi des grandes nombres de Nagaev en dimension infinie.- Hyperaccuracy of bootstrap based prediction.- Representation of Banach space valued martingales as stochastic integrals.- Nonlinear functional of empirical measures and the bootstrap.- Sur la régularité de certaines classes de fonctions aléatoires.- Comparison of log-probabilities of partial sums with those of Poissonized sums.- A law of large numbers for random vectors having large norms.- Uniform convergence of Martingales.- Continuity in lp of certain Ornstein-Uhlenbeck processes.- On the rate of convergence for the weighted empirical process.- Infinite-dimensional distributions in the thermodynamic limit of graph-valued Markov processes and the phenomenon of postgelation sticking.- An application of series representations to zero-one laws for infinitely divisible random vectors.- Strong approximations for set-indexed partial-sum processes and empirical processes of mixing random fields.- The law of the iterated logarithm for subsequences in Banach spaces.- Center, scale and asymptotic normality for sums of independent random variables.