Mixing Limit Theorems of Maximum of Absolute Sums and their Convergence Rates

Ibrahim A. Ahmad ()
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Ibrahim A. Ahmad: Colgate University

Journal of Theoretical Probability, 2005, vol. 18, issue 4, 813-826

Abstract: Conditioned, in the sense of Rényi (Acta Math. Acad. Sci. Hungar. 9, 215–228 1958), limit theorem in the L p -norm of the maximum of absolute sums of independent identically distributed random variables is established and its exact rate of convergence is given. The results are equivalent to establishing analogous results for the supremum of random functions of partial sums defined on C[0,1], i.e., the invariance principle. New methodologies are used to prove the results that are profoundly different from those used in Rényi (Acta Math. Acad. Sci. Hungar. 9, 215–228, 1958) and subsequent authors in proving the conditioned central limit theorem for partial sums.

Keywords: Invariance principle; mixing limit theorems; rates of convergence; L p -convergence; absolute maximum sum. (search for similar items in EconPapers)
Date: 2005
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DOI: 10.1007/s10959-005-7526-2

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