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

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