A strong limit theorem on gambling systems |
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| Authors: | Wen Liu Jinting Wang |
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| Institution: | a Department of Mathematics, Hebei University of Technology, Tianjin 300130, People's Republic of China;b Department of Mathematics, Northern Jiaotong University, Beijing 100044, People's Republic of China |
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| Abstract: | A strong limit theorem on gambling system for Bernoulli sequences is extended to the sequences of arbitrary discrete random variables by using the conditional probabilities. Furthermore, by allowing the selection function to take values in an interval, the conception of random selection is generalized. In the proof an approach of applying the differentiation of measure on a net to the investigation of the strong limit theorem is proposed. |
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| Keywords: | Strong limit theorem Gambling system Selection function |
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