Convergence of sequences of pairwise independent random variables
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- by N. Etemadi and A. Lenzhen PDF
- Proc. Amer. Math. Soc. 132 (2004), 1201-1202 Request permission
Abstract:
In spite of the fact that the tail $\sigma$-algebra of a sequence of pairwise independent random variables may not be trivial, we have discovered that if such a sequence converges in probability or almost everywhere, then the limit has to be a constant. This enables us to provide necessary and sufficient conditions for its convergence, in terms of its marginal distribution functions.References
- Kai Lai Chung, A course in probability theory, 2nd ed., Probability and Mathematical Statistics, Vol. 21, Academic Press [Harcourt Brace Jovanovich, Publishers], New York-London, 1974. MR 0346858
- James B. Robertson and James M. Womack, A pairwise independent stationary stochastic process, Statist. Probab. Lett. 3 (1985), no. 4, 195–199. MR 801689, DOI 10.1016/0167-7152(85)90017-3
Additional Information
- N. Etemadi
- Affiliation: Department of Mathematics, Statistics, and Computer Science (M/C 249), 322 Science and Engineering Offices, 851 South Morgan Street, Chicago, Illinois 60607-7045
- Email: etemadi@uic.edu
- A. Lenzhen
- Affiliation: Department of Mathematics, Statistics, and Computer Science (M/C 249), 322 Science and Engineering Offices, 851 South Morgan Street, Chicago, Illinois 60607-7045
- Email: lenzhen@math.uic.edu
- Received by editor(s): September 26, 2002
- Received by editor(s) in revised form: November 18, 2002
- Published electronically: September 11, 2003
- Communicated by: Richard C. Bradley
- © Copyright 2003 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 132 (2004), 1201-1202
- MSC (2000): Primary 60F15
- DOI: https://doi.org/10.1090/S0002-9939-03-07236-8
- MathSciNet review: 2045438