The PDF file you selected should load here if your Web browser has a PDF reader plug-in installed (for example, a recent version of Adobe Acrobat Reader).

Alternatively, you can also download the PDF file directly to your computer, from where it can be opened using a PDF reader. To download the PDF, click the Download link below.

If you would like more information about how to print, save, and work with PDFs, Highwire Press provides a helpful Frequently Asked Questions about PDFs.

Download this PDF file Fullscreen Fullscreen Off

References

  1. R.M. Balan and R. Kulik. Self-normalized weak invariance principle for mixing sequences. Tech. Rep. Series, Lab. Research Stat. Probab., Carleton University-University of Ottawa 417 (2005). Math. Review number not available.
  2. N.H. Bingham, C.M. Goldie and J.L. Teugels. Regular Variation. (1987) Cambridge University Press, Cambridge. Math. Review 91a:26003
  3. R.C. Bradley. Basic properties of strong mixing conditions. A survey and some open questions. Probability Surveys 2 (2005), 107-144. Math. Review MR2178042
  4. M. Csörgö, B. Szyszkowicz and Q. Wang. Donsker's theorem for self-normalized partial sum processes. Ann. Probab. 31 (2003), 1228-1240. Math. Review 2004h:60031
  5. W. Feller. An extension of the law of the iterated logarithm to variables without variance. J. Math. Mech. 18 1968, 343-355. Math. Review 0233399
  6. W. Feller. An introduction to probability theory and its applications. Vol. II. Second Edition. (1971), John Wiley, New York. Math. Review 0270403
  7. P. Hall and C.C.Heyde. Martingale limit theory and its applications. (1980) Academic Press, New York. Math. Review 83a:60001
  8. H. Kesten. Sums of independent random variables - without moment conditions. Ann. Math. Stat. 43 (1972), 701-732. Math. Review MR0301786
  9. H. Kesten and R.A. Maller. Some effects of trimming on the law of the iterated logarithm. J. Appl. Probab. 41A (2004), 253-271. Math. Review 2005a:60038
  10. M. Loève. Probability theory. Vol. II. Fourth Edition. (1978) Springer, New York. Math. Review MR0651018
  11. J. Mijnheer. A strong approximation of partial sums of i.i.d. random variables with infinite variance. Z. Wahrsch. verw. Gebiete 52 (1980), 1-7. Math. Review 81e:60032
  12. S. Y. Novak. On self-normalized sums and Student's statistic. Theory Probab. Appl. 49 (2005), 336-344. Math. Review 2005m:60038
  13. W. Philipp and W.F. Stout. Almost sure invariance principles for partial sums of weakly dependent random variables. Mem. AMS. Vol. 2 161 (1975). Math. Review MR0433597
  14. Q.-M. Shao. Almost sure invariance principles for mixing sequences of random variables. Stoch. Proc. Appl. 48 (1993), 319-334. Math. Review 95c:60030
  15. Q.-M. Shao. An invariance principle for stationary rho-mixing sequences with infinite variance. Chin. Ann. Math. Ser. B. 14 (1993), 27-42. Math. Review 94f:60051
Bookmark and Share


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