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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 Ergodic process ： ウィキペディア英語版 Ergodic process In econometrics and signal processing, a stochastic process is said to be ergodic if its statistical properties can be deduced from a single, sufficiently long, random sample of the process. The reasoning is that any collection of random samples from a process must represent the average statistical properties of the entire process. In other words, regardless of what the individual samples are, a birds-eye view of the collection of samples must represent the whole process. Conversely, a process that is not ergodic is a process that changes erratically at an inconsistent rate.〔Originally due to L. Boltzmann. See part 2 of ('Ergoden' on p.89 in the 1923 reprint.) It was used to prove equipartition of energy in the kinetic theory of gases〕 == Specific definitions == One can discuss the ergodicity of various statistics of a stochastic process. For example, a wide-sense stationary process $X(t)$ has constant mean :$\backslash mu\_X=\; E()$, and autocovariance :$r\_X(\backslash tau)\; =\; E((X(t+\backslash tau)-\backslash mu\_X))$, that depends only on the lag $\backslash tau$ and not on time $t$. The properties $\backslash mu\_X$ and $r\_X(\backslash tau)$ are ensemble averages not time averages. The process $X(t)$ is said to be mean-ergodic〔Papoulis, p.428〕 or mean-square ergodic in the first moment〔Porat, p.14〕 if the time average estimate :$\backslash hat\_X\; =\; \backslash frac\; \backslash int\_^\; X(t)\; \backslash ,\; dt$ converges in squared mean to the ensemble average $\backslash mu\_X$ as $T\; \backslash rightarrow\; \backslash infty$. Likewise, the process is said to be autocovariance-ergodic or mean-square ergodic in the second moment〔 if the time average estimate :$\backslash hat\_X(\backslash tau)\; =\; \backslash frac\; \backslash int\_^\; ()\; ()\; \backslash ,\; dt$ converges in squared mean to the ensemble average $r\_X(\backslash tau)$, as $T\; \backslash rightarrow\; \backslash infty$. A process which is ergodic in the mean and autocovariance is sometimes called ergodic in the wide sense.〔 An important example of an ergodic processes is the stationary Gaussian process with continuous spectrum. 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「Ergodic process」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.