We prove asymptotic results for a modification of the cross-entropy estimator originally introduced by Ziv and Merhav in the Markovian setting in 1993. Our results concern a more general class of decoupled measures. In particular, our results imply strong asymptotic consistency of the modified estimator for all pairs of functions of stationary, irreducible, finite-state Markov chains satisfying a mild decay condition. {Our approach is based on the study of a rescaled cumulant-generating function called the cross-entropic pressure, importing to information theory some techniques from the study of large deviations within the thermodynamic formalism.

翻译：我们证明了由Ziv和Merhav于1993年在马尔可夫框架下提出的交叉熵估计量的一种修正形式的渐近结果。该结果适用于一类更广泛的解耦测度。特别地，我们的结果意味着对于所有满足温和衰减条件的平稳、不可约、有限状态马尔可夫链的函数对，该修正估计量具有强渐近一致性。我们的方法基于对一种称为交叉熵压力的重标度累积生成函数的研究，将热力学形式中大偏差分析的技术引入信息论领域。