Acta Scientiarum Naturalium Universitatis Pekinensis

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On the Monotonicity of Autocorrelation Function for Finite State Markov Processes

CHEN Yong   

  1. Department of Applied Sciences, Peking University Health Science Center, Beijing 100083,
  • Received:2008-01-26 Online:2009-01-20 Published:2009-01-20



  1. 北京大学医学部医用理学系,北京100083,

Abstract: By using the Jordan decomposition of the generator (transition rate matrix), the difference in terms of the autocorrelation function between the reversibility and the irreversibility is shown. For a finite state Markov process with continuous time, its irreversibility implies that there exists an observable function on its state space such that its autocorrelation function is nonmonotonic over [0,∞) and negative at certain time interval; its reversibility implies that all the autocorrelation functions are monotonic and positive over [0,∞).

Key words: finite state Markov processes, autocorrelation function, reversible (detailed balance), oscillatory behavior

摘要: 使用生成元(转移速率矩阵)的若当分解,给出了以自相关函数描述的可逆性和不可逆性之间的区别。对于有限状态的马氏过程,证明了不可逆性蕴涵着存在状态空间上的实值观测函数,使得它的自相关函数在[0,∞)上不单调,且在某个时间间隔内,它是负值的;而可逆性则蕴涵着状态空间上所有的实值观测函数的自相关函数在[0,∞)上单调,且为正值的。

关键词: 有限状态马氏过程, 自相关函数, 可逆(细致平衡), 振荡行为

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