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Some small deviation theorems for arbitrary continuous random sequence

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Abstract

Let (X n) n∈N be a sequence of arbitrary continuous random variables, by the notion of relative entropy \(h_\mu ^{\tilde \mu } (\omega )\) as a measure of dissimilarity between probability measure μ and reference measure \(\tilde \mu \), the explicit, general bounds for the partial sums of arbitrary continuous random variables under suitable conditions are developed. The argument uses the known and elementary lemma of convergence for likelihood ratio.

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Authors and Affiliations

  1. Faculty of Mathematics & Physics, Anhui University of Technology, Ma’anshan, 243002, China

    Wang Zhongzhi

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  1. Wang Zhongzhi
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Additional information

Supported by the NNSF of China(10571076) and Anhui High Education Research Grant(2006Kj246B).

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Wang, Z. Some small deviation theorems for arbitrary continuous random sequence. Appl. Math. Chin. Univ. 22, 101–108 (2007). https://doi.org/10.1007/s11766-007-0013-z

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  • DOI: https://doi.org/10.1007/s11766-007-0013-z

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