鞅和信息散度

International Symposium on Information Theory and its Applications. International Symposium on Information Theory and its Applications Pub Date : 2005-10-31 DOI:10.1109/ISIT.2005.1523315

P. Harremoës

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引用次数: 2

摘要

证明了非负鞅的一个新的极大不等式。它加强了Doob的一个著名的极大不等式，并证明了所述不等式是紧的。不等式强调了鞅与信息发散之间的关系。它暗示了X log X有界鞅的逐点收敛。一个类似的不等式也适用于遍历序列。给出了与Shannon-McMillan-Breiman定理和Markov链的关系

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Martingales and information divergence

A new maximal inequality for non-negative martingales is proved. It strengthens a well-known maximal inequality by Doob, and it is demonstrated that the stated inequality is tight. The inequality emphasizes the relation between martingales and information divergence. It implies pointwise convergence of X log X bounded martingales. A similar inequality holds for ergodic sequences. Relations to the Shannon-McMillan-Breiman theorem and Markov chains are mentioned

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International Symposium on Information Theory and its Applications. International Symposium on Information Theory and its Applications

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