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Almost sure central limit theorems under minimal conditions

István Berkes, Endre Csáki and Lajos Horvath

Statistics & Probability Letters, 1998, vol. 37, issue 1, 67-76

Abstract: Let X1, X2,... be independent, identically distributed random variables with EX1 = 0, EX12 = 1 and let Sn = [summation operator]k[less-than-or-equals, slant]n Xk. We give nearly optimal criteria for an (unbounded) measurable function f to satisfy the a.s. central limit theorem, i.e., a.s., where [phi] is the standard normal density function.

Keywords: Logarithmic; average; Wiener; process; a.s.; central; limit; theorem (search for similar items in EconPapers)
Date: 1998
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