| 关于三状态马氏过程的复函数的功率谱密度（英） |
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| 引用本文： | 匡能晖,陈勇.关于三状态马氏过程的复函数的功率谱密度（英）[J].华东师范大学学报(自然科学版),2010,2010(3):134-142. |
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| 作者姓名： | 匡能晖 陈勇 |
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| 作者单位： | 湖南科技大学,数学与计算科学学院,湖南,湘潭,411201 |
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| 基金项目： | 湖南省教育厅资助科研项目 |
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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.
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| 关 键 词： | 功率谱密度 自相关函数 非平衡稳定状态 三状态马氏过程 功率谱密度 自相关函数 非平衡稳定状态 三状态马氏过程 |
| 收稿时间： | 2009-9-22 |
| 修稿时间： | 2010-1-12 |
On the fluctuation spectra with respect to complex functions of the three-state Markov processes |
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| KUANG Neng-hui,CHEN Yong.On the fluctuation spectra with respect to complex functions of the three-state Markov processes[J].Journal of East China Normal University(Natural Science),2010,2010(3):134-142. |
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| Authors: | KUANG Neng-hui CHEN Yong |
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| Institution: | School of Mathematics and Computing Science; Hunan University of Science and Technology，Xiangtan Hunan 411201, China |
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| 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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| Keywords: | power spectral density autocorrelation function nonequilibrium steady state three-state Markov processes |
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