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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 and time constant has the following properties. Exponential autocorrelation: : A power spectral density (PSD) function that has the same shape as the Cauchy distribution: : (Note that the Cauchy distribution and this spectrum differ by scale factors.) The above yields the following spectral factorization: : 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
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