We generalize to a broader class of decoupled measures a result of Ziv and Merhav on universal estimation of the specific cross (or relative) entropy, originally for a pair of multi-level Markov measures. Our generalization focuses on abstract decoupling conditions and covers pairs of suitably regular g-measures and pairs of equilibrium measures arising from the “small space of interactions” in mathematical statistical mechanics.
Barnfield, N., Grondin, R., Pozzoli, G., Raquépas, R. (2024). On the Ziv-Merhav Theorem beyond Markovianity I. CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES, 1-25 [10.4153/s0008414x24000178].
On the Ziv-Merhav Theorem beyond Markovianity I
Pozzoli, G;
2024
Abstract
We generalize to a broader class of decoupled measures a result of Ziv and Merhav on universal estimation of the specific cross (or relative) entropy, originally for a pair of multi-level Markov measures. Our generalization focuses on abstract decoupling conditions and covers pairs of suitably regular g-measures and pairs of equilibrium measures arising from the “small space of interactions” in mathematical statistical mechanics.
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