Springer Series in Statistics

Convergence of Stochastic Processes

Authors: Pollard, D.

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About this book

A more accurate title for this book might be: An Exposition of Selected Parts of Empirical Process Theory, With Related Interesting Facts About Weak Convergence, and Applications to Mathematical Statistics. The high points are Chapters II and VII, which describe some of the developments inspired by Richard Dudley's 1978 paper. There I explain the combinatorial ideas and approximation methods that are needed to prove maximal inequalities for empirical processes indexed by classes of sets or classes of functions. The material is somewhat arbitrarily divided into results used to prove consistency theorems and results used to prove central limit theorems. This has allowed me to put the easier material in Chapter II, with the hope of enticing the casual reader to delve deeper. Chapters III through VI deal with more classical material, as seen from a different perspective. The novelties are: convergence for measures that don't live on borel a-fields; the joys of working with the uniform metric on D[O, IJ; and finite-dimensional approximation as the unifying idea behind weak convergence. Uniform tightness reappears in disguise as a condition that justifies the finite-dimensional approximation. Only later is it exploited as a method for proving the existence of limit distributions. The last chapter has a heuristic flavor. I didn't want to confuse the martingale issues with the martingale facts.

Table of contents (1 chapter)

  • Martingales

    David Pollard

    Pages 170-187

    Buy Chapter $29.95
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Buy this book

eBook $89.99 net
( price for USA )
  • ISBN 978-1-4612-5254-2
  • digitally watermarked, no DRM
  • included format: PDF
  • eBooks can be used on all Reading Devices
Softcover $119.00 net
( price for USA )
  • ISBN 978-1-4612-9758-1
  • free shipping for individuals worldwide
  • usually dispatched within 3 to 5 business days

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Bibliographic Information

Bibliographic Information
Book Title
Convergence of Stochastic Processes
Series Title
Springer Series in Statistics
Copyright
1984
Publisher
Springer-Verlag New York
Copyright Holder
Springer-Verlag New York Inc.
eBook ISBN
978-1-4612-5254-2
DOI
10.1007/978-1-4612-5254-2
Softcover ISBN
978-1-4612-9758-1
Series ISSN
0172-7397
Edition Number
1
Topics