A Supplement to the Einmahl–Li Results on Two-Sided Iterated Logarithm Type Behavior for I.I.D. Random Variables

REFERENCES

• Bulinskii˘ , A.V. , and Dil'man , S.V. 2002 . Universal normalization and the law of the iterated logarithm . Uspekhi Matematicheskikh Nauk 57 : 193 – 194 . [in Russian; English translation in Russian Mathematical Surveys 57:418–419] .
   Google Scholar
• Einmahl , U. 1988 . Strong approximations for partial sums of i.i.d. B-valued r.v.'s in the domain of attraction of a Gaussian law . Probability Theory and Related Fields 77 : 65 – 85 .
   Google Scholar
• Einmahl , U. 2007 . A generalization of Strassen's functional LIL . Journal of Theoretical Probability 20 : 901 – 915 .
   Web of Science ®Google Scholar
• Einmahl , U. , and Li , D. 2005 . Some results on two-sided LIL behavior . Annals of Probability 33 : 1601 – 1624 .
   Web of Science ®Google Scholar
• Feller , W. 1968 . An extension of the law of the iterated logarithm to variables without variance . Journal of Mathematics and Mechanics 18 : 343 – 355 .
   Google Scholar
• Hartman , P. , and Wintner , A. 1941 . On the law of the iterated logarithm . American Journal of Mathematics 63 : 169 – 176 .
   Google Scholar
• Heyde , C.C. 1968. A converse to the iterated logarithm law. Journal of Applied Probability 5:210–215.
   Google Scholar
• Klesov , O. , and Rosalsky , A. 2001 . A nonclassical law of the iterated logarithm for i.i.d. square integrable random variables . Stochastic Analysis and Applications 19 : 627 – 641 .
   Web of Science ®Google Scholar
• Klesov , O. , and Rosalsky , A. 2002 . A nonclassical law of the iterated logarithm for i.i.d. square integrable random variables. II . Stochastic Analysis and Applications 20 : 839 – 846 .
   Web of Science ®Google Scholar
• Li , D. , Qi , Y. , and Rosalsky , A. 2007 . Some results on one-sided iterated logarithm type behavior . Acta Scientiarum Mathematicarum (Szeged) 73 : 367 – 395 .
   Google Scholar
• Steiger , W.L. , and Zaremba , S.K. 1972 . The converse of the Hartman–Wintner theorem . Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete 22 : 193 – 194 .
   Google Scholar
• Strassen , V. 1966 . A converse to the law of the iterated logarithm . Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete 4 : 265 – 268 .
   Google Scholar