Progress in Probability

High Dimensional Probability II

Editors: Giné, Evarist, Mason, David M., Wellner, Jon A. (Eds.)

Buy this book

eBook $179.00
price for USA (gross)
  • ISBN 978-1-4612-1358-1
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $289.00
price for USA
  • ISBN 978-0-8176-4160-3
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $229.00
price for USA
  • ISBN 978-1-4612-7111-6
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this book

High dimensional probability, in the sense that encompasses the topics rep­ resented in this volume, began about thirty years ago with research in two related areas: limit theorems for sums of independent Banach space valued random vectors and general Gaussian processes. An important feature in these past research studies has been the fact that they highlighted the es­ sential probabilistic nature of the problems considered. In part, this was because, by working on a general Banach space, one had to discard the extra, and often extraneous, structure imposed by random variables taking values in a Euclidean space, or by processes being indexed by sets in R or Rd. Doing this led to striking advances, particularly in Gaussian process theory. It also led to the creation or introduction of powerful new tools, such as randomization, decoupling, moment and exponential inequalities, chaining, isoperimetry and concentration of measure, which apply to areas well beyond those for which they were created. The general theory of em­ pirical processes, with its vast applications in statistics, the study of local times of Markov processes, certain problems in harmonic analysis, and the general theory of stochastic processes are just several of the broad areas in which Gaussian process techniques and techniques from probability in Banach spaces have made a substantial impact. Parallel to this work on probability in Banach spaces, classical proba­ bility and empirical process theory were enriched by the development of powerful results in strong approximations.

Table of contents (32 chapters)

  • Moment Bounds for Self-Normalized Martingales

    Peña, Victor H. (et al.)

    Pages 3-11

  • Exponential and Moment Inequalities for U-Statistics

    Giné, Evarist (et al.)

    Pages 13-38

  • A Multiplicative Inequality for Concentration Functions of n-Fold Convolutions

    Götze, Friedrich (et al.)

    Pages 39-47

  • On Exact Maximal Khinchine Inequalities

    Pinelis, Iosif

    Pages 49-63

  • Strong Exponential Integrability of Martingales with Increments Bounded by a Sequence of Numbers

    Rosiński, Jan

    Pages 65-76

Buy this book

eBook $179.00
price for USA (gross)
  • ISBN 978-1-4612-1358-1
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $289.00
price for USA
  • ISBN 978-0-8176-4160-3
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $229.00
price for USA
  • ISBN 978-1-4612-7111-6
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Loading...

Recommended for you

Loading...

Bibliographic Information

Bibliographic Information
Book Title
High Dimensional Probability II
Editors
  • Evarist Giné
  • David M. Mason
  • Jon A. Wellner
Series Title
Progress in Probability
Series Volume
47
Copyright
2000
Publisher
Birkhäuser Basel
Copyright Holder
Springer Science+Business Media New York
eBook ISBN
978-1-4612-1358-1
DOI
10.1007/978-1-4612-1358-1
Hardcover ISBN
978-0-8176-4160-3
Softcover ISBN
978-1-4612-7111-6
Series ISSN
1050-6977
Edition Number
1
Number of Pages
XI, 512
Topics