References
- de Acosta , A. 1983 . A new proof of the Hartman–Wintner law of the iterated logarithm . Annals of Probability 11 : 270 – 276 .
- Billingsley , P. 1995 . Probability and Measure. , 3rd ed. John Wiley , New York .
- Chow , Y.S. , and Teicher , H. 1997 . Probability Theory: Independence, Interchangeability, Martingales. , 3rd ed. Springer-Verlag , New York .
- Csörgo , M. , and Révész , P. 1981 . Strong Approximations in Probability and Statistics . Academic Press , New York .
- Diaconis , P. , and Freedman , D. 1999 . Iterated random functions . SIAM Review 41 : 45 – 76 .
- Egorov , V.A. 1971 . A generalization of the Hartman–Wintner theorem on the law of the iterated logarithm. Vestnik Leningradskogo Universiteta No. 7:22–28. [In Russian; English translation in Vestnik Leningrad University. Mathematics 4:117–124.]
- Einmahl , U. , and Li , D. 2005 . Some results on two-sided LIL behavior . Annals of Probability 33 : 1601 – 1624 .
- Erdös , P. 1939 . On a family of symmetric Bernoulli convolutions . American Journal of Mathematics 61 : 974 – 976 .
- Garsia , A.M. 1962 . Arithmetic properties of Bernoulli convolutions . Transactions of the American Mathematical Society 102 : 409 – 432 .
- Hartman , P. , and Wintner , A. 1941 . On the law of the iterated logarithm . American Journal of Mathematics 63 : 169 – 176 .
- Heyde , C.C. 1969. Some properties of metrics in a study on convergence to normality. Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete 11:181–192.
- Jessen , B. , and Wintner , A. 1935 . Distribution functions and the Riemann zeta function . Transactions of the American Mathematical Society 38 : 48 – 88 .
- Peres , Y. , and Solomyak , B. 1996 . Absolute continuity of Bernoulli convolutions, a simple proof . Mathematical Research Letters 3 : 231 – 239 .
- Peres , Y. , and Solomyak , B. 1998 . Self-similar measures and intersections of Cantor sets . Transactions of the American Mathematical Society 350 : 4065 – 4087 .
- Petrov , V.V. 1995 . Limit Theorems of Probability Theory: Sequences of Independent Random Variables . Clarendon Press/Oxford University Press , New York .
- Rosalsky , A. 1981 . Lim sup behavior of sums of geometrically weighted i.i.d. random variables . Stochastic Processes and their Applications 11 : 297 – 300 .
- Royden , H.L. 1968 . Real Analysis. , 2nd ed. Macmillan , New York .
- Solomyak , B. 1995 . On the random series (an Erdös problem) . Annals of Mathematics, Second Series 142 : 611 – 625 .
- Stout , W.F. 1974 . Almost Sure Convergence . Academic Press , New York .
- Strassen , V. 1964 . An invariance principle for the law of the iterated logarithm . Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete 3 : 211 – 226 .
- Teicher , H. 1974 . On the law of the iterated logarithm . Annals of Probability 2 : 714 – 728 .