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.

A Sandwich Proof of the Shannon-McMillan-Breiman Theorem

Paul H. Algoet and Thomas M. Cover
The Annals of Probability
Vol. 16, No. 2 (Apr., 1988), pp. 899-909
Stable URL: http://www.jstor.org/stable/2243846
Page Count: 11
  • 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.
A Sandwich Proof of the Shannon-McMillan-Breiman Theorem
Preview not available

Abstract

Let {Xt} be a stationary ergodic process with distribution P admitting densities p(x0,..., xn-1) relative to a reference measure M that is finite order Markov with stationary transition kernel. Let IM(P) denote the relative entropy rate. Then n-1log p(X0,..., Xn-1) → IM(P) a.s. (P). We present an elementary proof of the Shannon-McMillan-Breiman theorem and the preceding generalization, obviating the need to verify integrability conditions and also covering the case IM(P) = ∞. A sandwich argument reduces the proof to direct applications of the ergodic theorem.

Page Thumbnails

  • Thumbnail: Page 
899
    899
  • Thumbnail: Page 
900
    900
  • Thumbnail: Page 
901
    901
  • Thumbnail: Page 
902
    902
  • Thumbnail: Page 
903
    903
  • Thumbnail: Page 
904
    904
  • Thumbnail: Page 
905
    905
  • Thumbnail: Page 
906
    906
  • Thumbnail: Page 
907
    907
  • Thumbnail: Page 
908
    908
  • Thumbnail: Page 
909
    909