Progress in Probability

By: Joergen Hoffmann-Joergensen (Editor), Michael B. Marcus (Editor), Jon A. Wellner (Editor)

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Hardcover | 27 November 2003

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360 Pages

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23.5 x 15.88 x 2.54

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The title High Dimensional Probability is an attempt to describe the many trib- utaries of research on Gaussian processes and probability in Banach spaces that started in the early 1970's. In each of these fields it is necessary to consider large classes of stochastic processes under minimal conditions. There are rewards in re- search of this sort. One can often gain deep insights, even about familiar processes, by stripping away details that in hindsight turn out to be extraneous. Many of the problems that motivated researchers in the 1970's were solved. But the powerful new tools created for their solution, such as randomization, isoperimetry, concentration of measure, moment and exponential inequalities, chaining, series representations and decoupling turned out to be applicable to other important areas of probability. They led to significant advances in the study of empirical processes and other topics in theoretical statistics and to a new ap- proach to the study of aspects of Levy processes and Markov processes in general. Papers on these topics as well as on the continuing study of Gaussian processes and probability in Banach are included in this volume.

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Preface
Stochastic inequalities and perfect independence	p. 3
Prokhorov-LeCam-Varadarajan's compactness criteria for vector measures on metric spaces	p. 35
On measures in locally convex spaces	p. 43
Karhunen-Loeve expansions for weighted Wiener processes and Brownian bridges via Bessel functions	p. 57
Extension du theoreme de Cameron-Martin aux translations aleatoires. II. Integrabilite des densites	p. 95
Rates of convergence for Levy's modulus of continuity and Hinchin's law of the iterated logarithm	p. 105
On the limit set in the law of the iterated logarithm for U-statistics of order two	p. 111
Perturbation approach applied to the asymptotic study of random operators	p. 127
A uniform functional law of the logarithm for a local Gaussian process	p. 135
Strong limit theorems for mixing random variables with values in Hilbert space and their applications	p. 153
Table of Contents provided by Blackwell. All Rights Reserved.

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