A NONCLASSICAL LAW OF THE ITERATED LOGARITHM FOR I.I.D. SQUARE INTEGRABLE RANDOM VARIABLES

REFERENCES

• de Acosta , A. 1983 . A new proof of the Hartman-Wintner law of the iterated logarithm . Ann. Probab. , 11 : 270 – 276 .
   Web of Science ®Google Scholar
• Bulinskii , A. V. 1977 . On normalization in the law of the iterated logarithm, Teor. Veroyatnost . i Primen. , 22 : 407 – 409 .
   Google Scholar
• 1977 . In Russian, English translation in Theory Probab. Appl. , 22 : 398 – 399 .
   Google Scholar
• Chow , Y. S. , Teicher , H. , Wei , C. Z. and Yu , K. F. 1981 . Iterated logarithm laws with random subsequences . Z. Wahrsch. Verw. Gebiete , 57 : 235 – 251 .
   Web of Science ®Google Scholar
• Csörgő , M. and Révész , P. 1981 . Strong Approximations in Probability and Statistics New York : Academic Press .
   Google Scholar
• Egorov , V. A. 1971 . A generalization of the Hartman-Wintner theorem on the law of the iterated logarithm . Vestnik Leningrad. Univ. , 7 : 22 – 28 .
   Google Scholar
• 1977 . In Russian, English translation in Vestnik Leningrad Univ. Math. , 4 : 117 – 124 .
   Google Scholar
• Feller , W. 1943 . The general form of the so-called law of the iterated logarithm . Trans. Amer. Math. Soc. , 54 : 373 – 402 .
   Google Scholar
• Feller , W. 1968 . An extension of the law of the iterated logarithm to variables without variance . J. Math. Mech. , 18 : 343 – 356 .
   Google Scholar
• Gut , A. 1986 . Law of the iterated logarithm for subsequences . Probab. Math. Statist. , 7 : 27 – 58 .
   Google Scholar
• Hartman , P. and Wintner , A. 1941 . On the law of the iterated logarithm . Amer. J. Math. , 63 : 169 – 176 .
   Google Scholar
• Heyde , C. C. 1968 . On the converse to the iterated logarithm law . J. Appl. Probab. , 5 : 210 – 215 .
   Google Scholar
• Heyde , C. C. 1969 . Some properties of metrics in a study on convergence to normality . Z. Wahrsch. Verw. Gebiete , 11 : 181 – 192 .
   Web of Science ®Google Scholar
• Kesten , H. 1972 . Sums of independent random variables—without moment conditions . Ann. Math. Statist. , 43 : 701 – 732 .
   Google Scholar
• Knopp , K. 1951 . Theory and Application of Infinite Series , 2nd English ed. London : Blackie and Son .
   Google Scholar
• Martikainen , A. I. 1980 . A converse to the law of the iterated logarithm for a random walk . Teor. Veroyatnost. i Primen. , 25 : 364 – 366 .
   Google Scholar
• 1981 . In Russian, English translation in Theory Probab. Appl. , 25 : 361 – 362 .
   Google Scholar
• Petrov , V. V. 1975 . Sums of Independent Random Variables Berlin : Springer-Verlag .
   Google Scholar
• Petrov , V. V. 1992 . On the law of the iterated logarithm for a sequence of independent random variables . Zap. Nauchn. Sem. S.-Petersburg. Otdel. Mat. Inst. Steklov. (POMI) , 194 : 134–137, 179 – 180 . In Russian
   Google Scholar
• Pruitt , W. E. 1981 . General one-sided laws of the iterated logarithm . Ann. Probab. , 9 : 1 – 48 .
   Web of Science ®Google Scholar
• Qualls , C. 1977 . The law of the iterated logarithm on arbitrary sequences for stationary Gaussian processes and Brownian motion . Ann. Probab. , 5 : 724 – 739 .
   Google Scholar
• Rosalsky , A. 1980 . On the converse to the iterated logarithm law . Sankhyā Ser. A , 42 : 103 – 108 .
   Google Scholar
• Rosalsky , A. 1981 . A generalization of the iterated logarithm law for weighted sums with infinite variance . Z. Wahrsch. Verw. Gebiete , 58 : 351 – 372 .
   Google Scholar
• Steiger , W. L. and Zaremba , S. K. 1972 . The converse of the Hartman-Wintner theorem . Z. Wahrsch. Verw. Gebiete , 22 : 193 – 194 .
   Google Scholar
• Strassen , V. 1964 . An invariance principle for the law of the iterated logarithm . Z. Wahrsch. Verw. Gebiete , 3 : 211 – 226 .
   Google Scholar
• Strassen , V. 1966 . A converse to the law of the iterated logarithm . Z. Wahrsch. Verw. Gebiete , 4 : 265 – 268 .
   Google Scholar
• Teicher , H. 1974 . On the law of the iterated logarithm . Ann. Probab. , 2 : 714 – 728 .
   Web of Science ®Google Scholar