Some universal results on the behavior of increments of partial sums

Annals of Probability

Volumn 24, Issue 3, 1996, Pages 1388-1407

  Einmahl, Uwe ^a   Mason, David M ^b  

^a INDIANA UNIVERSITY   (United States)

^b UNIVERSITY OF DELAWARE   (United States)

Author keywords

Increments of partial sums; Maximal inequalities; Quantile transformation; Universal law of the iterated logarithm

Indexed keywords

EID: 0030371765     PISSN: 00911798     EISSN: None     Source Type: Journal    
DOI: 10.1214/aop/1065725186     Document Type: Article

References (15)

1. BILLINGSLEY, P. (1986). Probability and Measure 2nd ed. Wiley, New York.
2. CHOW, Y. S. and TEICHER, H. (1988). Probability Theory: Independence, Interchangeability, Martingales, 2nd ed. Springer, New York.
3. CSÖRGO, M. and RÉVÉSZ, P. (1979). How big are the increments of a Wiener process? Ann. Probab. 7 731-737.
4. CSÖRGO, M. and RÉVÉSZ, P. (1981). Strong Approximations in Probability and Statistics. Academic Press, New York.
5. CSÖRGO, S., HÄUSLER, E. and MASON, D. M. (1988a). A probabilistic approach to the asymptotic distribution of sums of independent, identically distributed random variables. Adv. in Appl. Math. 9 259-333.
6. CSÖRGO, S., HÄUSLER, E. and MASON, D. M. (1988b). The asymptotic distribution of trimmed sums. Ann. Probab. 16 672-699.
7. DUDLEY, R. M. (1984). A course on empirical processes. In Ecole d'Éte de Probabilites de Saint-Flour XII-1982. Lecture Notes in Math. 1097 2-142. Springer, Berlin.
8. EINMAHL, U. and MASON, D. M. (1994). A universal Chung-type law of the iterated logarithm. Ann. Probab. 22 1803-1825.
9. HANSON, D. L. and RUSSO, R. P. (1983). Some results on increments of the Wiener process with applications to lag sums of i.i.d. random variables. Ann. Probab. 11 609-623.
10. n ↓ 0. Proc. Sixth Berkeley Symp. Math. Statist. Probab. 1 227-244. Univ. California Press.
11. KLASS, M. (1976). Toward a universal law of the iterated logarithm. I. Z. Wahrsch. Verw. Gebiete. 36 165-178.
12. LAI, T. L. (1974). Limit theorems for delayed sums. Ann. Probab. 2 432-440.
13. MASON, D. M. (1994). A universal one-sided law of the iterated logarithm. Ann. Probab. 22 1826-1837.
14. PRUITT, W. E. (1981). General one-sided laws of the iterated logarithm. Ann. Probab. 9 1-48.
15. ROTHMANN, M. D. and RUSSO, R. P. (1993). A series criterion for moving maxima. Stochastic Process. Appl. 46 241-247.