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An invariance principle for mixing sequences of random variables

  • Walter Philipp
  • Geoffrey R. Webb
Article

Keywords

Stochastic Process Probability Theory Mathematical Biology Invariance Principle 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Billingsley, P.: Convergence of probability measures. New York: Wiley 1968.Google Scholar
  2. 2.
    Gikhman, I.I., Skorokhod, A.V.: Introduction to the theory of random processes. Philadelphia: Saunders 1969.Google Scholar
  3. 3.
    Ibragimov, I.A.: Some limit theorems for stationary processes. Theor. Probab. Appl. 7, 349–382 (1962).Google Scholar
  4. 4.
    Iosifescu, M., Theodorescu, R.: Random processes and learning. Berlin-Heidelberg-New York: Springer 1969.Google Scholar
  5. 5.
    Loève, M.: Probability theory. 3rd. ed. Princeton: Van Nostrand 1963.Google Scholar
  6. 6.
    Philipp, W.: The central limit problem for mixing sequences or random variables. Z.Wahrscheinichkeitstheorie verw. Geb. 12, 155–171 (1969).Google Scholar
  7. 7.
    Philipp, W.: The law of iterated logarithm for mixing stochastic processes. Ann. Math. Statist. 40, 1985–1991 (1969).Google Scholar
  8. 8.
    Philipp, W.: Mixing sequences of random variables and probabilistic number theory. Memoirs AMS vol. 114, Providence 1971.Google Scholar
  9. 9.
    Prohorov, Yu.V.: Convergence of random processes and limit theorems in probability theory. Theor. Probab. Appl. 1, 157–214 (1956).Google Scholar
  10. 10.
    Webb, G.: The functional central limit theorem for nonstationary sequences of mixing random variables. Ph. D. Thesis, Duke University, Durham, N.C., 1970.Google Scholar

Copyright information

© Springer-Verlag 1973

Authors and Affiliations

  • Walter Philipp
    • 1
  • Geoffrey R. Webb
    • 2
  1. 1.Department of MathematicsUniversity of IllinoisUrbanaUSA
  2. 2.Department of MathematicsMemphis State UniversityMemphisUSA

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