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Almost sure invariance principles for partial sums of weakly dependent random variables

About this Title

Walter Philipp and William Stout

Publication: Memoirs of the American Mathematical Society
Publication Year: 1975; Volume 2, Number 161
ISBNs: 978-0-8218-1861-9 (print); 978-1-4704-0547-2 (online)
DOI: https://doi.org/10.1090/memo/0161
MathSciNet review: 0433597

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Table of Contents

Chapters

  • 1. Introduction
  • 2. Description of the method
  • 3. Lacunary trigonometric series with unweighted summands
  • 4. Stationary $\phi$-mixing sequences
  • 5. Gaussian sequences
  • 6. Lacunary trigonometric series with weights
  • 7. Functions of strongly mixing random variables
  • 8. Nonstationary mixing sequences
  • 9. A refinement of the Shannon-McMillan-Breiman theorem
  • 10. Markov sequences
  • 11. Retarded asymptotic martingale difference sequences
  • 12. Continuous parameter stochastic processes
  • Appendix I. The Gaal-Koksma strong law of large numbers
  • Appendix I. An example