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Journal of Mathematics
Volume 2013, Article ID 640137, 6 pages
http://dx.doi.org/10.1155/2013/640137
Research Article

Functional Limit Theorem for Products of Sums of Independent and Nonidentically Distributed Random Variables

Institute of Mathematics, Maria Curie-Skłodowska University, Plac M.C.-Skłodowskiej 1, 20-031 Lublin, Poland

Received 27 August 2012; Accepted 11 November 2012

Academic Editor: Inés Couso

Copyright © 2013 Przemysław Matuła and Iwona Stępień. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. B. C. Arnold and J. A. Villaseñor, “The asymptotic distributions of sums of records,” Extremes, vol. 1, no. 3, pp. 351–363, 1999. View at Publisher · View at Google Scholar · View at MathSciNet
  2. G. Rempała and J. Wesołowski, “Asymptotics for products of sums and U-statistics,” Electronic Communications in Probability, vol. 7, pp. 47–54, 2002. View at Publisher · View at Google Scholar · View at MathSciNet
  3. L.-X. Zhang and W. Huang, “A note on the invariance principle of the product of sums of random variables,” Electronic Communications in Probability, vol. 12, pp. 51–56, 2007. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. K. M. Kosiński, “On the functional limits for sums of a function of partial sums,” Statistics & Probability Letters, vol. 79, no. 13, pp. 1522–1527, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. P. Matuła and I. Stępień, “Weak convergence of products of sums of independent and non-identically distributed random variables,” Journal of Mathematical Analysis and Applications, vol. 353, no. 1, pp. 49–54, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. G. R. Shorack and J. A. Wellner, Empirical Processes with Applications to Statistics, John Wiley & Sons Inc., New York, NY, USA, 1986. View at MathSciNet
  7. P. Billingsley, Convergence of Probability Measures, John Wiley & Sons, New York, NY, USA, 1968. View at MathSciNet
  8. R. M. Dudley, Real Analysis and Probability, Cambridge Studies in Advanced Mathematics, Cambridge University, Cambridge, Uk, 2002. View at Publisher · View at Google Scholar · View at MathSciNet
  9. W. J. Kaczor and M. T. Nowak, Problems in Mathematical Analysis. I, American Mathematical Society, Providence, RI, USA, 2000. View at MathSciNet