Asymptotics for dependent Bernoulli random variables |
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Authors: | Lan WuYongcheng Qi Jingping Yang |
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Institution: | a LMAM, Department of Financial Mathematics, Center for Statistical Science, Peking University, Beijing 100871, Chinab Department of Mathematics and Statistics, University of Minnesota Duluth, 1117 University Drive, Duluth, MN 55812, USA |
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Abstract: | This paper considers a sequence of Bernoulli random variables which are dependent in a way that the success probability of a trial conditional on the previous trials depends on the total number of successes achieved prior to the trial. The paper investigates almost sure behaviors for the sequence and proves the strong law of large numbers under weak conditions. For linear probability functions, the paper also obtains the strong law of large numbers, the central limit theorems and the law of the iterated logarithm, extending the results by James et al. (2008). |
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Keywords: | 60F15 |
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