On the fluctuation spectra with respect to complex functions ofthe three-state Markov processes
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摘要: 得到了关于不可约的三状态马氏过程的复函数的自相关函数与功率谱密度的显式表达式.由三次和五次方程理论得到: 当转移速率矩阵存在相同的特征值时,给出复函数的功率谱密度在[0,+∞)上非单调的一个充要条件;当转移速率矩阵存在不同的非零特征值时,给出复函数的功率谱密度在[0,+∞) 上非单调的一些充分条件.Abstract: Explicit formulae for the autocorrelation functions and the fluctuation spectra with respect to complex functions of the irreducible three-state Markov processes were investigated. By the theory of cubic and quintic equations, the necessary and sufficient condition for the fluctuation spectra with respect to complex functions to be nonmonotonic on [0,+∞) was presented when there existed coinciding eigenvalues for the transition rate matrix, and the sufficient conditions for the fluctuation spectra with respect to complex functions to be nonmonotonic on [0,+∞)were given when there existed distinct nonzero eigenvalues.
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