标题： 返回时间的大型偏差及相关熵估计量在位移空间上 显示英文标题

标题： Large deviations of return times and related entropy estimators on shift spaces

摘要： 我们证明了基于有限字母上的移位空间上的返回时间和等待时间的几种熵和交叉熵估计量的大偏差原理。 我们考虑满足某些解耦条件的移位不变概率测度，这些条件不包含任何形式的混合性或遍历性。 我们建立了不同估计量的速率函数之间的精确关系，以及这些速率函数与相应压力之间的关系，其中一个是Rényi熵函数。 对于最常用的返回时间定义，大偏差速率函数被证明是非凸的，除非在边缘情况下。 这些结果特别适用于不可约马尔可夫链、Bowen正则势能的平衡测度、g-测度、统计力学中绝对可和相互作用的不变吉布斯态，也适用于可能远离吉布斯性的概率测度，包括一些隐马尔可夫模型和重复量子测量过程。 显示英文摘要

摘要： We prove the large deviation principle for several entropy and cross entropy estimators based on return times and waiting times on shift spaces over finite alphabets. We consider shift-invariant probability measures satisfying some decoupling conditions which imply no form of mixing nor ergodicity. We establish precise relations between the rate functions of the different estimators, and between these rate functions and the corresponding pressures, one of which is the R\'enyi entropy function. For the most commonly used definition of return times, the large-deviation rate function is proved to be nonconvex, except in marginal cases. The results apply in particular to irreducible Markov chains, equilibrium measures for Bowen-regular potentials, g-measures, invariant Gibbs states for absolutely summable interactions in statistical mechanics, and also to probability measures which may be far from Gibbsian, including some hidden Markov models and repeated quantum measurement processes.