Self-Normalized LIL for Hanson–Russo Type Increments |
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| Authors: | Han-Ying Liang Josef G Steinebach |
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| Institution: | 1. Department of Applied Mathematics, Tongji University, Shanghai, 200092, P.R. China
2. Mathematical Institute, University of Cologne, D-50 931, K?ln, Germany
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| Abstract: | Let X
1, X
2,... be independent, but not necessarily identically distributed random variables in the domain of attraction of a normal law or a stable law with index 0 < α < 2. Using suitable self-normalizing (or Studentizing) factors, laws of the iterated logarithm for self-normalized Hanson–Russo type increments are discussed. Also, some analogous results for self-normalized weighted sums of i.i.d. random variables are given. |
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| Keywords: | Self-normalized sum law of the iterated logarithm Hanson– Russo type increment weighted sum |
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