A new strong invariance principle for sums of independent random vectors

Journal of Mathematical Sciences

Volumn 163, Issue 4, 2009, Pages 311-327

  Einmahl, U ^a  

^a VRIJE UNIVERSITEIT BRUSSEL   (Belgium)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 70549103375     PISSN: 10723374     EISSN: 15738795     Source Type: Journal    
DOI: 10.1007/s10958-009-9676-8     Document Type: Article

References (16)

1. E. Berger, "Fast sichere Approximation von Partialsummen unabhängiger und stationärer ergodischer Folgen von Zufallsvektoren," Dissertation, Univ. Göttingen (1982).
2. R. Bhatia, Matrix Analysis, Springer, New York (1997).
3. U. Einmahl, "Strong invariance principles for partial sums of independent random vectors," Ann. Probab., 15, 1419-1440 (1987).
4. U. Einmahl, "A useful estimate in the multidimensional invariance principle," Probab. Theory Relat. Fields, 76, 81-101 (1987).
5. U. Einmahl, "Extensions of results of Komlós, Major, and Tusnády to the multivariate case," J. Multivar. Anal., 28, 20-68 (1989).
6. U. Einmahl, "A generalization of Strassen's functional LIL," J. Theor. Probab., 20, 901-915 (2007).
7. U. Einmahl and D. Li, "Some results on two-sided LIL behavior," Ann. Probab., 33, 1601-1624 (2005).
8. U. Einmahl and D. Li, "Characterization of LIL behavior in Banach space," Trans. Amer. Math. Sac., 360, 6677-6693 (2008).
9. U. Einmahl and D. M. Mason, "Rates of clustering in Strassen's LIL for partial sum processes," Probab. Theory Relat. Fields, 97, 479-487 (1993).
10. J. Komlós, P. Major, and G. Tusnády, "An approximation of partial sums of independent r. v.'s and the sample d. f.. II," Z. Wahrsch. Verw. Gebiete, 34, 33-58 (1976).
11. P. Major, "The approximation of partial sums of independent r. v.'s.," Z. Wahrsch. Verw. Gebiete, 35, 213-220 (1976).
12. P. Major, "An improvment of Strassen's invariance principle" Ann. Probab., 7, 55-61 (1979).
13. W. Philipp, "Almost sure invariance principles for sums of B-valued random variables" Lect. Notes Math., 709, 171-193 (1979).
14. A. I. Sakhanenko, "A new way to obtain estimates in the invariance principle," in: High-Dimensional Probability II, Progress in Probability, 7, Birkhäuser, Boston (2000), pp. 223-245.
15. V. Strassen, "An invariance principle for the law of the iterated logarithm," Z. Wahrsch. Verw. Gebiete, 3, 211-226 (1964).
16. A. Zaitsev, "Multidimensional version of the results of Komlós, Major, and Tusnády for vectors with finite exponential moments," ESAIM Probab. Statist., 2, 41-108 (1998).