Access

You are not currently logged in.

Access your personal account or get JSTOR access through your library or other institution:

login

Log in to your personal account or through your institution.

If You Use a Screen Reader

This content is available through Read Online (Free) program, which relies on page scans. Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.

Approximation, Metric Entropy and Small Ball Estimates for Gaussian Measures

Wenbo V. Li and Werner Linde
The Annals of Probability
Vol. 27, No. 3 (Jul., 1999), pp. 1556-1578
Stable URL: http://www.jstor.org/stable/2652814
Page Count: 23
  • Read Online (Free)
  • Download ($19.00)
  • Subscribe ($19.50)
  • Cite this Item
Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Approximation, Metric Entropy and Small Ball Estimates for Gaussian Measures
Preview not available

Abstract

A precise link proved by Kuelbs and Li relates the small ball behavior of a Gaussian measure μ on a Banach space E with the metric entropy behavior of Kμ, the unit ball of the reproducing kernel Hilbert space of μ in E. We remove the main regularity assumption imposed on the unknown function in the link. This enables the application of tools and results from functional analysis to small ball problems and leads to small ball estimates of general algebraic type as well as to new estimates for concrete Gaussian processes. Moreover, we show that the small ball behavior of a Gaussian process is also tightly connected with the speed of approximation by "finite rank" processes.

Page Thumbnails

  • Thumbnail: Page 
1556
    1556
  • Thumbnail: Page 
1557
    1557
  • Thumbnail: Page 
1558
    1558
  • Thumbnail: Page 
1559
    1559
  • Thumbnail: Page 
1560
    1560
  • Thumbnail: Page 
1561
    1561
  • Thumbnail: Page 
1562
    1562
  • Thumbnail: Page 
1563
    1563
  • Thumbnail: Page 
1564
    1564
  • Thumbnail: Page 
1565
    1565
  • Thumbnail: Page 
1566
    1566
  • Thumbnail: Page 
1567
    1567
  • Thumbnail: Page 
1568
    1568
  • Thumbnail: Page 
1569
    1569
  • Thumbnail: Page 
1570
    1570
  • Thumbnail: Page 
1571
    1571
  • Thumbnail: Page 
1572
    1572
  • Thumbnail: Page 
1573
    1573
  • Thumbnail: Page 
1574
    1574
  • Thumbnail: Page 
1575
    1575
  • Thumbnail: Page 
1576
    1576
  • Thumbnail: Page 
1577
    1577
  • Thumbnail: Page 
1578
    1578