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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Entropy rate ： ウィキペディア英語版 Entropy rate In the mathematical theory of probability, the entropy rate or source information rate of a stochastic process is, informally, the time density of the average information in a stochastic process. For stochastic processes with a countable index, the entropy rate ''H''(''X'') is the limit of the joint entropy of ''n'' members of the process ''X''''k'' divided by ''n'', as ''n'' tends to infinity: :$H(X)\; =\; \backslash lim\_\; \backslash frac\; H(X\_1,\; X\_2,\; \backslash dots\; X\_n)$ when the limit exists. An alternative, related quantity is: :$H\text{'}(X)\; =\; \backslash lim\_\; H(X\_n|X\_,\; X\_,\; \backslash dots\; X\_1)$ For strongly stationary stochastic processes, $H(X)\; =\; H\text{'}(X)$. The entropy rate can be thought of as a general property of stochastic sources; this is the asymptotic equipartition property. == Entropy rates for Markov chains == Since a stochastic process defined by a Markov chain that is irreducible and aperiodic and persistent has a stationary distribution, the entropy rate is independent of the initial distribution. For example, for such a Markov chain ''Y''''k'' defined on a countable number of states, given the transition matrix ''P''''ij'', ''H''(''Y'') is given by: :$\backslash displaystyle\; H(Y)\; =\; -\; \backslash sum\_\; \backslash mu\_i\; P\_\; \backslash log\; P\_$ where ''μ''''i'' is the stationary distribution of the chain. A simple consequence of this definition is that an i.i.d. stochastic process has an entropy rate that is the same as the entropy of any individual member of the process. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Entropy rate」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.