Abstract We consider a sequence of correlated Bernoulli variables whose probability of success of the current trial depends conditionally on the previous trials as a linear function of the sample mean. We extend the results of Zhang and Zhang (2015) by establishing an almost sure invariance principle and a weak invariance principle in a larger setting. Moreover, we also state a Gaussian fluctuation related to an almost sure and L p convergence for the model.

中文翻译：

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相关伯努利随机变量的一些极限定理

摘要 我们考虑一系列相关的伯努利变量，其当前试验的成功概率有条件地取决于作为样本均值的线性函数的先前试验。我们通过在更大的环境中建立几乎肯定的不变性原则和弱不变性原则来扩展 Zhang 和 Zhang（2015）的结果。此外，我们还说明了与模型的几乎确定和 L p 收敛相关的高斯波动。