Strong Laws for Martingale Differences and Independent Random Variables

Journal of Theoretical Probability

Volumn 11, Issue 4, 1998, Pages 979-995

  Teicher, Henry ^a  

^a RUTGERS UNIVERSITY   (United States)

Author keywords

Conditional variances; Martingale differences; Strong laws

Indexed keywords

EID: 0032283245     PISSN: 08949840     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1022616915799     Document Type: Article

References (15)

1. Chow, Y. S., and Teicher, H. (1978). Probability Theory: Independence, Interchangeability, Martingales, Springer-Verlag, New York.
2. Chow, Y. S. (1965). Local convergence of martingales and the law of large numbers. Ann. Math. Statist. 36, 552-558.
3. Egorov, V. A. (1970). On the strong law of large numbers and the law of the iterated logarithm for sequence of independent random variables. Theory Prob. Appl. 15, 509-514.
4. Fernholz, L., and Teicher, H. (1980). Stability of random variables and iterated logarithm laws for martingales and quadratic forms. Ann. Prob. 8, 765-774.
5. Freedman, D. L. (1973). Another note on the Borel-Cantelli lemma and the strong law with the Poisson approximation as a by-product. Ann. Prob. 1, 910-925.
6. Freedman, D. L. (1975). On tail probabilities for martingales. Ann. Prob. 3, 100-118.
7. Hall, P., and Heyde, C. C. (1980). Martingale Limit Theory and Its Application, Academic Press, New York.
8. Jain, N. C., Jogdeo, K., and Stout, W. F. (1975). Upper and lower functions for martingales and mixing processes. Ann. Prob. 3, 119-145.
9. Meyer, P. (1972). Martingales and Stochastic Integrals, Springer-Verlag, New York.
10. Philipp, W., and Stout, W. F. (1986). Invariance principles for martingales and sums of independent random variables. Math. Zeit. 192, 253-264.
11. Stout, W. F. (1973). Maximal inequalities and the law of the iterated logarithm. Ann. Prob, 1, 322-328.
12. Teicher, H. (1968). Some new conditions for the strong law. Proc. Nat. Acad. Sci. U.S.A. 59, 705-707.
13. Teicher, H. (1974). On the law of the iterated logarithm. Ann. Prob. 2, 714-728.
14. Teicher, H. (1979). Generalized exponentials bounds, iterated logarithm and strong laws. Z. Wahr. und verw. Geb. 48, 293-307.
15. Zhang, C.-H. (1986). The lower limit of a normalized random walk. Ann. Prob. 14, 560-581.