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- W2033672007 abstract "Let ${X_t}$ be a stationary ergodic process with distribution $P$ admitting densities $p(x_0,ldots, x_{n-1})$ relative to a reference measure $M$ that is finite order Markov with stationary transition kernel. Let $I_M(P)$ denote the relative entropy rate. Then $n^{-1}log p(X_0,ldots, X_{n-1}) rightarrow I_M(P) mathrm{a.s.} (P).$ We present an elementary proof of the Shannon-McMillan-Breiman theorem and the preceding generalization, obviating the need to verify integrability conditions and also covering the case $I_M(P) = infty$. A sandwich argument reduces the proof to direct applications of the ergodic theorem." @default.
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- W2033672007 modified "2023-10-02" @default.
- W2033672007 title "A Sandwich Proof of the Shannon-McMillan-Breiman Theorem" @default.
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- W2033672007 doi "https://doi.org/10.1214/aop/1176991794" @default.
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