Communications for Statistical Applications and Methods

The Korean Statistical Society (한국통계학회)
권호 표지
DOI QR코드

DOI QR Code

The Uniform Law of Large Numbers for the Baker Transformation

  • Published : 2009.01.31
Download PDF
⟨ Previous Next ⟩

Abstract

The baker transformation is an ergodic transformation defined on the half open unit square. This paper considers the limiting behavior of the partial sum process of a martingale sequence constructed from the baker transformation. We get the uniform law of large numbers for the baker transformation.

Keywords

References

  1. DeHardt, J. (1971). Generalizations of the Glivenko-Cantelli theorem, The Annals of Mathematical and Statistics, 42, 2050-2055 https://doi.org/10.1214/aoms/1177693073
  2. Durrett, R. (1991). Probability: Theory and Examples, Wadsworth, California
  3. Hoffmann-J$\o$rgensen, J. (1991). Stochastic processes on Polish spaces, Aarhus Universitet, Matema-tisk Institut
  4. Van de Geer, S. (2000). Empirical Processes in M-Estimation, Cambridge University Press, Cam-bridge
  5. Van der Vaart, A. W. and Wellner, J. A. (1996). Weak Convergence and Empirical Processes with Applications to Statistics, Springer-Verlag, New York