A note on the invariance principle of the product of sums of random variables

Wei Huang (Zhejiang University)
Li-Xin Zhang (Zhejiang University)

Abstract


The central limit theorem for the product of sums of various random variables has been studied in a variety of settings. The purpose of this note is to show that this kind of result is a corollary of the invariance principle.

Full Text: Download PDF | View PDF online (requires PDF plugin)

Pages: 51-56

Publication Date: March 14, 2007

DOI: 10.1214/ECP.v12-1255

References

  1. B.C. Arnold and J. A. Villase ñ or. The Asymptotic Distributions of Sums of Records. Extremes , 1 , No. 3 (1998), 351-363. MR1814709 (2002a:60025)

  2. P. Billingsley. Convergence of Probability Measures, Joh Wiley & Sons, INC, New York (1999).

  3. M. Csörgö and P. Révész . StrongApproximations in Probability and Statistics , Akadémiai Kiadó, Budapest (1981).

  4. K. Gonchigdanzan and G. A. Rempala. A note on the almost sure limit theorem for the product of partial sums. Applied Math. Lett . 19 , No. 2 (2006), 191-196. MR2198407
  5. G. Rempala and J. Wesolowski. Asymptotics for products of sums and U-statistics. Elect. Comm. in Prob., 7 (2002), 47-54. MR1887173 (2002k:60070)
  6. V. Strassen. An invariance principle for the law of the iterated logarithm. Z. Wahrsch. Keitsth. verw. Gebiete, 3 (1964), 211-226. MR0175194 (30 #5379)
Bookmark and Share


Creative Commons License
This work is licensed under a Creative Commons Attribution 3.0 License.