华东师范大学学报（自然科学版）
華東師範大學學報（自然科學版）
화동사범대학학보（자연과학판）
JOURNAL OF EAST CHINA NORMAL UNIVERSITY(NATURAL SCIENCE)
2010年
3期
134-141
,共8页
功率谱密度%自相关函数%非平衡稳定状态%三状态马氏过程
功率譜密度%自相關函數%非平衡穩定狀態%三狀態馬氏過程
공솔보밀도%자상관함수%비평형은정상태%삼상태마씨과정
power spectral density%autocorrelation function%nonequilibrium steady state%three-state Markov processes
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.
得到瞭關于不可約的三狀態馬氏過程的複函數的自相關函數與功率譜密度的顯式錶達式.由三次和五次方程理論得到:噹轉移速率矩陣存在相同的特徵值時,給齣複函數的功率譜密度在[0,+∞)上非單調的一箇充要條件;噹轉移速率矩陣存在不同的非零特徵值時,給齣複函數的功率譜密度在[0,+∞)上非單調的一些充分條件.
득도료관우불가약적삼상태마씨과정적복함수적자상관함수여공솔보밀도적현식표체식.유삼차화오차방정이론득도:당전이속솔구진존재상동적특정치시,급출복함수적공솔보밀도재[0,+∞)상비단조적일개충요조건;당전이속솔구진존재불동적비령특정치시,급출복함수적공솔보밀도재[0,+∞)상비단조적일사충분조건.
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.
