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小第166行：
第166行： − + − 此时，对于任意的<math>j</math>，有<math>\sum_j q_{ij}=\frac{\sum\pi_j p_{ji}}{\pi_i}=\frac{\pi}{\pi}=1</math>。+
→细致平衡条件
\frac{P(X_n=j)P(X_{n+1}=i|X_n=j)P(X_{n+2},\ldots|X_{n+1}=i,X_n=j)}{P(X_{n+1}=i)P(X_{n+2},\ldots|X_{n+1}=i)}=
\frac{P(X_n=j)P(X_{n+1}=i|X_n=j)P(X_{n+2},\ldots|X_{n+1}=i,X_n=j)}{P(X_{n+1}=i)P(X_{n+2},\ldots|X_{n+1}=i)}=
\frac{P(X_n=j)P(X_{n+1}=i|X_n=j)}{P(X_{n+1}=i)}=\frac{\pi_jp_{ji}}{\pi_i}=
\frac{P(X_n=j)P(X_{n+1}=i|X_n=j)}{P(X_{n+1}=i)}=\frac{\pi_jp_{ji}}{\pi_i}=
P(X_n=j|X_{n+1}=i)=\triangleq q_{ij}</math>。
P(X_n=j|X_{n+1}=i)\triangleq q_{ij}</math>。
即反向过程仍满足马尔科夫性质。此时，对于任意的<math>j</math>，有<math>\sum_j q_{ij}=\frac{\sum\pi_j p_{ji}}{\pi_i}=\frac{\pi}{\pi}=1</math>。