翻訳と辞書 Words near each other ・ Gauss–Bonnet gravity ・ Gauss–Bonnet theorem ・ Gauss–Codazzi equations ・ Gauss–Hermite quadrature ・ Gauss–Jacobi quadrature ・ Gauss–Kronrod quadrature formula ・ Gauss–Krüger coordinate system ・ Gauss–Kuzmin distribution ・ Gauss–Kuzmin–Wirsing operator ・ Gauss–Laguerre quadrature ・ Gauss–Legendre algorithm ・ Gauss–Legendre method ・ Gauss–Lucas theorem ・ Gauss–Manin connection ・ Gauss–Markov ・ Gauss–Markov process ・ Gauss–Markov theorem ・ Gauss–Newton algorithm ・ Gauss–Seidel method ・ Gaustad ・ Gaustad (station) ・ Gaustad Hospital ・ Gaustadalléen (station) ・ Gaustadt ・ Gaustatoppen ・ Gausturm ・ Gausvik ・ Gausvik Church ・ Gausón ・ Gaut Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Gauss–Markov process ： ウィキペディア英語版 Gauss–Markov process Gauss–Markov stochastic processes (named after Carl Friedrich Gauss and Andrey Markov) are stochastic processes that satisfy the requirements for both Gaussian processes and Markov processes. The stationary Gauss–Markov process is a very special case because it is unique, except for some trivial exceptions. Every Gauss–Markov process ''X''(''t'') possesses the three following properties: # If ''h''(''t'') is a non-zero scalar function of ''t'', then ''Z''(''t'') = ''h''(''t'')''X''(''t'') is also a Gauss–Markov process # If ''f''(''t'') is a non-decreasing scalar function of ''t'', then ''Z''(''t'') = ''X''(''f''(''t'')) is also a Gauss–Markov process # There exists a non-zero scalar function ''h''(''t'') and a non-decreasing scalar function ''f''(''t'') such that ''X''(''t'') = ''h''(''t'')''W''(''f''(''t'')), where ''W''(''t'') is the standard Wiener process. Property (3) means that every Gauss–Markov process can be synthesized from the standard Wiener process (SWP). ==Properties of the Stationary Gauss-Markov Processes== A stationary Gauss–Markov process with variance $\backslash textbf(X^(t))\; =\; \backslash sigma^$ and time constant $\backslash beta^$ has the following properties. Exponential autocorrelation: :$\backslash textbf\_(\backslash tau)\; =\; \backslash sigma^e^.\backslash ,$ A power spectral density (PSD) function that has the same shape as the Cauchy distribution: :$\backslash textbf\_(j\backslash omega)\; =\; \backslash frac\}.\backslash ,$ (Note that the Cauchy distribution and this spectrum differ by scale factors.) The above yields the following spectral factorization: :$\backslash textbf\_(s)\; =\; \backslash frac\}$ = \frac \cdot\frac. which is important in Wiener filtering and other areas. There are also some trivial exceptions to all of the above. 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「Gauss–Markov 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.