华东师范大学学报(自然科学版) ›› 2010, Vol. 2010 ›› Issue (3): 134-142.

• 应用数学与基础数学 • 上一篇    下一篇

关于三状态马氏过程的复函数的功率谱密度（英）

匡能晖,陈勇   

  1. 湖南科技大学数学与计算科学学院,湖南,湘潭411201
  • 收稿日期:2009-09-22 修回日期:2010-01-12 出版日期:2010-05-25 发布日期:2010-05-25
  • 通讯作者: 匡能晖

On the fluctuation spectra with respect to complex functions ofthe three-state Markov processes

KUANG Neng-hui, CHEN Yong   

  1. School of Mathematics and Computing Science; Hunan University of Science and Technology，Xiangtan Hunan 411201, China
  • Received:2009-09-22 Revised:2010-01-12 Online:2010-05-25 Published:2010-05-25
  • Contact: KUANG Neng-hui

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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.

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

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.

Key words: autocorrelation function, nonequilibrium, steady state, three-state Markov processes, power spectral density, autocorrelation function, nonequilibrium, steady state, three-state Markov processes

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