Moderate deviations and Erdös-Rényi-Shepp laws for weighted sums |
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| Authors: | Fuqing Gao |
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| Institution: | School of Mathematics and Statistics, Wuhan University, Wuhan 430072, PR China |
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| Abstract: | Let X0,X1,… be i.i.d. random variables with E(X0)=0, E(X20)=1 and E(exp{tX0})<∞ for any |t|<t0. We prove that the weighted sums V(n)=∑j=0∞aj(n)Xj, n?1 obey a moderately large deviation principle if the weights satisfy certain regularity conditions. Then we prove a new version of the Erdös-Rényi-Shepp laws for the weighted sums. |
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| Keywords: | Moderate deviations Large deviations Erdö s-Ré nyi-Shepp laws Weighted sums i i d random variables |
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