The Law of the Logarithm for Weighted Sums of Independent Random Variables

D. Li and R. J. Tomkins ()
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D. Li: Lakehead University
R. J. Tomkins: University of Regina, Regina

Journal of Theoretical Probability, 2003, vol. 16, issue 3, 519-542

Abstract: Abstract Let X,X n ;n≥1 be a sequence of real-valued i.i.d. random variables with E(X)=0. Assume B(u) is positive, strictly increasing and regularly-varying at infinity with index 1/2≤α x) = o(\log x){\text{ }}as{\text{ x}} \to \infty $$ and $$\mathop {\lim }\limits_{x \to \infty } \sup \frac{{n\log nE(X^2 I_{\left\{ {X^2

Keywords: law of the iterated logarithm; law of the logarithm; strong law of large numbers; weighted sums (search for similar items in EconPapers)
Date: 2003
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DOI: 10.1023/A:1025684513749

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