High Dimensional Probability

ISBN-13: 9783034897907 / Angielski / Miękka / 2012 / 335 str.

Ernst Eberlein; Marjorie Hahn

Opis

What is high dimensional probability? Under this broad term one finds a collection of topics associated by the fact that n plays a key role in each, whether the idea of high dimension n is expressed in the problem or in the methods by which it is approached. For example, the study of probability in Banach spaces gave impetus to a number of methods whose importance has gone far beyond the original goal of extending limit laws to the vector valued case. Familiar applications are in the areas of empirical processes, the use of majorizing measures to study regularity of stochastic processes, and the theory of concentration of measure. Many of the new ideas, results and directions of this newly evolving field were explored on a broad front at the Conference on High Dimensional Probability held at Oberwolfach in August 1996. The papers in this volume are marked by vitality and diversity and will give researchers and graduate students in probability or statistics much to whet their interest."

Spis treści

Weak Convergence of the Row Sums of a Triangular Array of Empirical Processes.- Self-Normalized Large Deviations in Vector Spaces.- Consistency of M-Estimators and One-Sided Bracketing.- Small Deviation Probabilities of Sums of Independent Random Variables.- Strong Approximations to the Local Empirical Process.- On Random Measure Processes with Application to Smoothed Empirical Processes.- A Consequence for Random Polynomials of a Result of De La Peña and Montgomery-Smith.- Distinctions Between the Regular and Empirical Central Limit Theorems for Exchangeable Random Variables.- Laws of Large Numbers and Continuity of Processes.- Convergence in Law of Random Elements and Random Sets.- Asymptotics of Spectral Projections of Some Random Matrices Approximating Integral Operators.- A Short Proof of the Gaussian Isoperimetric Inequality.- Some Shift Inequalities for Gaussian Measures.- A Central Limit Theorem for the Sock-Sorting Problem.- Oscillations of Gaussian Stein’s Elements.- A Sufficient Condition for the Continuity of High Order Gaussian Chaos Processes.- On Wald’s Equation and First Exit Times for Randomly Stopped Processes with Independent Increments.- The Best Doob-type Bounds for the Maximum of Brownian Paths.- Optimal Tail Comparison Based on Comparison of Moments.- The Bootstrap of Empirical Processes for ?-Mixing Sequences.