相依二元序列的更新模型
Renewal model for dependent binary sequences
AI总结：
提出用延迟更新过程构造平稳相依二元序列，可实现多种次指数相关衰减，并证明熵性质、大数定律与中心极限定理。
摘要：
我们建议通过将序列的两个符号之一与底层更新过程的更新时刻相关联，来构造无限随机二元序列。聚焦于对应延迟更新过程的平稳二元序列，我们研究了相关性以及该模型实现给定自协方差结构的能力，表明可以解释种类繁多的相关性次指数衰减。特别是，通过生成具有相关性多项式衰减和拉伸指数衰减的二元序列，测试了该方法的稳健性和效率。此外，为证明模型选择的最大熵原则合理，我们证明了典型序列的渐近等分性质，该性质自然导向等待时间分布的 Shannon 熵。为支持理论与数据的比较，我们针对一般可观测量的时间平均建立了大数定律和中心极限定理。
英文摘要：
We suggest to construct infinite stochastic binary sequences by associating one of the two symbols of the sequence with the renewal times of an underlying renewal process. Focusing on stationary binary sequences corresponding to delayed renewal processes, we investigate correlations and the ability of the model to implement a prescribed autocovariance structure, showing that a large variety of subexponential decay of correlations can be accounted for. In particular, robustness and efficiency of the method are tested by generating binary sequences with polynomial and stretched-exponential decay of correlations. Moreover, to justify the maximum entropy principle for model selection, an asymptotic equipartition property for typical sequences that naturally leads to the Shannon entropy of the waiting time distribution is demonstrated. To support the comparison of the theory with data, a law of large numbers and a central limit theorem are established for the time average of general observables.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
