Rocky Mountain Journal of Mathematics

A Skorohod Representation and an Invariance Principle for Sums of Weighted i.i.d. Random Variables

Evan Fisher

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Rocky Mountain J. Math., Volume 22, Number 1 (1992), 169-179.

First available in Project Euclid: 5 June 2007

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60F17: Functional limit theorems; invariance principles
Secondary: 60F15: Strong theorems 60G50: Sums of independent random variables; random walks

Skorohod representation sums of weighted i.i.d. random variables functional law of the iterated logarithm invariance principles


Fisher, Evan. A Skorohod Representation and an Invariance Principle for Sums of Weighted i.i.d. Random Variables. Rocky Mountain J. Math. 22 (1992), no. 1, 169--179. doi:10.1216/rmjm/1181072802.

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  • P. Billingsley, Probability and measure, Wiley, New York, 1979.
  • Y.S. Chow and H. Teicher, Iterated logarithm laws for weighted averages, Z. Wahrsch. Verw. Gebiete 26, (1973), 87-94.
  • --------, Probability theory, Springer-Verlag, New York, 1978.
  • L.T. Fernholz and H. Teicher, Stability of random variables and iterated logarithm laws for martingales and quadratic forms, Ann. Probab. 8 (1980), 765-774.
  • P. Hall and C.C. Heyde, Martingale limit theory and its application, Academic Press, New York, 1980.
  • C.C. Heyde and D.J. Scott, Invariance principles for the law of the iterated logarithm for martingales and processes with stationary increments, Ann. Probab. 1 (1973), 428-436.
  • N.C. Jain, K. Jogdeo, and W.F. Stout, Upper and lower functions for martingales and mixing processes, Ann. Probab. 3 (1975), 119-145.
  • B. Jamison, S. Orey, and W.E. Pruitt, Convergence of weighted averages of independent random variables, Z. Wahrsch. Verw. Gebiete 4 (1965), 40-44.
  • F.B. Knight, Essentials of Brownian motion and diffusion, Amer. Math. Soc. Math. Surveys 18, 1981.
  • A. Rosalsky, Lim sup behavior of sums of geometrically weighted i.i.d. random variables, Stochastic Processes Appl. 3 (1981), 297-300.
  • A.V. Skorohod, Studies in the theory of random processes, Addison-Wesley, Reading, MA, 1965.
  • W.F. Stout, Almost sure convergence, Academic Press, New York, 1974.
  • V. Strassen, An invariance principle for the law of the iterated logarithm, Z. Wahrsch. Verw. Gebiete 3 (1964), 211-226.
  • --------, Almost sure behavior of sums of independent random variables and martingales, Proc. 5th Berkeley Symp. Math. Statist. Probab. 2 (1967), 315-343.
  • H. Teicher, On the law of the iterated logarithm, Ann. Probab. 2 (1974), 714-728.
  • R.J. Tomkins, A law of the iterated logarithm for martingales, Z. Wahrsch. Verw. Gebiete. 33 (1975), 65-68.