논문KCI 등재
Precise rates in the law of the logarithm for the moment convergence of i.i.d. random variables
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초록
Let {X,Xn; n ≥ 1} be a sequence of i.i.d. random variables. Set Sn = X₁ + X₂ + ... + Xn, Mn =[수식] Then we obtain that for any -1 < b < 1/2, [수식] if and only if EX = 0 and EX² = σ² < ∞.
Abstract
Let {X,Xn; n ≥ 1} be a sequence of i.i.d. random variables. Set Sn = X₁ + X₂ + ... + Xn, Mn =[수식] Then we obtain that for any -1 < b < 1/2, [수식] if and only if EX = 0 and EX² = σ² < ∞.
참고문헌 (7)
- P. Billingsley, "Convergence of Probability Measures: Second edition, Wiley Series in Probability and Statistics: Probability and Statistics. A Wiley-Interscience Publication" (1999), John Wiley & Sons, Inc.
- M. Csorgo, "Strong Approximations in Probability and Statistics, Probability and Mathematical Statistics" (1981), Academic Press, Inc.
- U. Einmahl, "The Darling-Erdos theorem for sums of i.i.d. random variables, Probab", Theory Related Fields, 82(2), pp.241~257 (1989)
- W. Feller, "The law of the iterated logarithm for identically distributed random variables", Annals of Mathematics, 47, pp.631~638 (1946)
- A. Gut, "Precise asymptotics in the law of the iterated logarithm", Annals of Probability, 28(4), pp.1870~1883 (2000)
- A. I. Sakhanenko, "On estimates of the rate of convergence in the invariance principle, In Advances in Probability Theory: Limit Theorems and Related Problems", pp.124~135 (1984), Springer
- A. I. Sakhanenko, "Convergence rate in the invariance principle for nonidentically distributed variables with exponential moment, In Advances in Probability Theory: Limit Theorems for Sums of Random Variables", pp.2~73 (1985), Springer
관련 논문AI추천
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