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