The almost sure central limit theorems in the joint version for the maxima and sums of certain stationary Gaussian sequences

Statistics and Probability Letters

Volumn 78, Issue 4, 2008, Pages 347-357

  Dudziński, Marcin ^a  

^a WARSAW UNIVERSITY OF LIFE SCIENCES   (Poland)

Author keywords

Almost sure central limit theorem; Associated random variables; Extreme values; Karamata's theorem; Partial sums; Slowly varying functions at infinity; Stationary Gaussian sequences

Indexed keywords

EID: 39049135794     PISSN: 01677152     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.spl.2007.07.007     Document Type: Article

References (7)

1. Bagai I., and Prakasa Rao B.L.S. Estimation of the survival function for stationary associated processes. Statist. Probab. Lett. 12 (1991) 385-391
2. Csaki E., and Gonchigdanzan K. Almost sure limit theorems for the maximum of stationary Gaussian sequences. Statist. Probab. Lett. 58 (2002) 195-203
3. Ho H.C., and Hsing T. On the asymptotic joint distribution of the sum and maximum of stationary normal random variables. J. Appl. Probab. 33 (1996) 138-145
4. Leadbetter M.R., Lindgren G., and Rootzen H. Extremes and Related Properties of Random Sequences and Processes (1983), Springer, New York
5. Mielniczuk J. Some remarks on the almost sure central limit theorem for dependent sequences. Limit theorems in Probability and Statistics vol. 2 (2002), Janos Bolyai Mathematical Society, Budapest 391-403
6. Newman, C.M., 1984. Asymptotic independence and limit theorems for positively and negatively dependent random variables. In: Inequalities in Statistics and Probability, vol. 5. IMS Lecture Notes-Monograph Series, pp. 127-140.
7. Pitt L.D. Positively correlated normal variables are associated. Ann. Probab. 10 (1982) 496-499