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