武汉理工大学随机过程第5章(10)

5.1连续时间马尔可夫链

pij (t+ s )= P{ X (t+ s )= j| X (0)= i}=∑ P{ X ( t+ s )= j, X ( t )= k| X ( 0 )= i}=∑ P{ X (t+ s )= j| X (t )= k, X (0)= i}k∈I k∈I

P{ X (t )= k| X (0)= i}=∑ P{ X ( t+ s )= j| X ( t )= k} P{ X ( t )= k| X ( 0 )= i}=∑ pkj ( s ) pik (t )=∑ pik (t ) pkj ( s )k∈I

k∈I k∈I