Equivalent conditions of complete convergence for independent weighted sums

Science in China, Series A: Mathematics, Physics, Astronomy

Volumn 41, Issue 9, 1998, Pages 939-949

  Wang, Yuebao ^a   Liu, Xuguo ^b   Su, Chun ^c  

^a SOOCHOW UNIVERSITY   (China)

^b Zhanjiang Teachers College   (China)

^c UNIVERSITY OF SCIENCE AND TECHNOLOGY OF CHINA   (China)

Author keywords

Complete convergence; Equivalence; Independent weighted sum

Indexed keywords

EID: 0041740608     PISSN: 10069283     EISSN: None     Source Type: Journal    
DOI: 10.1007/bf02880003     Document Type: Article

References (13)

1. Hsu, P. L., Robbins, H., Complete convergence and the law of large numbers, Proc. Nat. Acad. Sci., 1947, 33(2): 25.
2. Erdös, P., On a theorem of Hsu and Robbins, Ann. Math. Statist., 1949, 20: 286.
3. Erdös, P., Remark on my paper "On a theorem of Hsu and Robbins", Ann. Math. Statist., 1950, 21: 138.
4. Spitzer, F. L., A combinatorial lemma and its applications to probability theory, Trans. Amer. Math. Soc., 1956, 82: 323.
5. Baum, L. E., Katz, M., Convergence rates in the law of large numbers, Trans. Amer. Math. Soc., 1965, 120(1): 108.
6. Bai, Z. D., Su, C., The complete convergence for partial sums of i. i. d. random variables, Sci. Sinica, Ser. A, 1985, 28: 1261.
7. Chow, Y. S., Some convergence theorems for independent random variables, Ann. Math. Statist., 1966, 37: 1482.
8. Stout, W. F., Almost Sure Convergence, New York: Academic Press, 1974.
9. Gut, A., Complete convergence and Cesaro summation for i. i. d. random variables, Probab., Theor. Relat. Fields, 1993, 97: 169.
10. Li, D. L., Rao, M. B., Jiang, T. F. et al., Complete convergence and almost sure convergence of weighted sums of random variables., J. Theor. Probab., 1995, 8: 49.
11. Hoffmann-Jørgensen, J., Sums of independent Banach space valued random variables, Studia Math ., 1974, 52: 159.
12. Petrov, V. V., Limit Theorems for Sums of Independent Random Variables (in Russian), Moscow: Nauka, 1987.
13. Wang, Q. Y., Further discussion on the complete convergence for independent sums of subsequences., Acta. Math. Scientia (in Chinese), 1993, 13(1): 37.