Self-normalized moderate deviations and lils

Stochastic Processes and their Applications

Volumn 75, Issue 1, 1998, Pages 51-65

  Dembo, Amir ^a   Shao, Qi Man ^b  

^a STANFORD UNIVERSITY   (United States)

^b UNIVERSITY OF OREGON   (United States)

Author keywords

60F15; Law of the iterated logarithm; Moderate deviations; Primary 60F10; Self normalized partial sums

Indexed keywords

EID: 0002361771     PISSN: 03044149     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0304-4149(98)00007-6     Document Type: Article

References (10)

1. Araujo, A., Giné, E., 1980. The Central Limit Theorem for Real and Banach Valued Random Variables. Wiley, New York.
2. Bingham, N.H., Goldie, C.M., Teugels, J.L., 1987. Regular variation. Cambridge University Press, Cambridge.
3. Christoph, G., Wolf, W., 1992. Convergence Theorems with a Stable Limit Law, vol. 70, Akademie Verlag, Germany.
4. p -valued Gaussian processes Ann. Probab. 21:1993;1958-1990.
5. Dembo, A., Zeitouni, O., 1998. Large Deviations Techniques and Applications. Second edition. Springer, New York.
6. Griffin P., Kuelbs J. Self-normalized laws of the iterated logarithm. Ann. Probab. 17:1989;1571-1601.
7. Jiang, T., 1995. Moderate deviations for double arrays with applications to moving average processes, Gaussian processes and Cesaro's sums. Preprint.
8. Nagaev A.V. Limit theorems including the effect of large deviations when Cramér's condition is violated. Isz. AN UzSSR, ser. fiz-matem. 6:1969;17-22.
9. Shao, Q.M., 1995. Self-normalized large deviations. Ann. Probab. 25, 285-328.
10. Vinogradov V.V. Asymptotic expansions of the probability of large deviations for sums of independent random variables under violation of Cramér's condition. Theor. Probab. Math. Statist. 31:1985;21-27.