更改

称状态空间<math>S=\{1,2,\ldots\}</math>上的随机过程<math>\{X_n,\ n=0,1,2,\ldots\}</math>是'''马尔科夫链'''或具有马尔科夫性质，若满足

称状态空间<math>S=\{1,2,\ldots\}</math>上的随机过程<math>\{X_n,\ n=0,1,2,\ldots\}</math>是'''马尔科夫链'''<ref name=":2">Brémaud P．Markov chains: Gibbs fields, Monte Carlo simulation, and queues．Springer Science & Business Media, 1999, 53-156.</ref>或具有马尔科夫性质，若满足

<math>\forall n,\ \ P(X_n=j|X_{n-1}=i,X_{n-2}=x_{n-2},\ldots,X_1=x_1)=P(X_n=j|X_{n-1}=i),</math>

<math>\forall n,\ \ P(X_n=j|X_{n-1}=i,X_{n-2}=x_{n-2},\ldots,X_1=x_1)=P(X_n=j|X_{n-1}=i),</math>

称状态空间<math>S=\{1,2,\ldots\}</math>上的随机过程<math>\{X_t,\ t\geq 0\}</math>是'''连续时间马尔科夫链'''，若满足

称状态空间<math>S=\{1,2,\ldots\}</math>上的随机过程<math>\{X_t,\ t\geq 0\}</math>是'''连续时间马尔科夫链'''<ref name=":3">Kendall D G, Batchelor G K, Bingham N H, Hayman W K, Hyland J M E, Lorentz G G, Moffatt H K, Parry W, Razborov A A, Robinson C A and Whittle P. Andrei Nikolaevich Kolmogorov (1903–1987). Bulletin of the London Mathematical Society, 1990, 22(1): 31-100.</ref>

，若满足

<math>\forall n,\ 0\leq t_0<t_1<\ldots<t_{n-1}<t_{n},\ \ P(X_{t_n}=j|X_{t_{n-1}}=i,X_{t_{n-2}}=x_{t_{n-2}},\ldots,X_{t_{0}}=x_{t_{0}})=P(X_{t_n}=j|X_{t_{n-1}}=i)</math>。

<math>\forall n,\ 0\leq t_0<t_1<\ldots<t_{n-1}<t_{n},\ \ P(X_{t_n}=j|X_{t_{n-1}}=i,X_{t_{n-2}}=x_{t_{n-2}},\ldots,X_{t_{0}}=x_{t_{0}})=P(X_{t_n}=j|X_{t_{n-1}}=i)</math>。