武汉理工大学随机过程第5章(16)

5.1连续时间马尔可夫链

定理5.2齐次马尔可夫过程的绝对概率及有限维概率分布具有下列性质： (1) pj(t)≥0 (2) (3)

∑ p (t )= 1 p (t )=∑ p p (t )j∈I j

j

(4) p j (t+τ )=∑ pi (t ) pij (τ )i∈I

i∈I

i

ij

p(t )= pP(t )

p (t+τ )= p (t ) P(τ )

(5) P{ X (t )= i, 1 1i∈I

=∑ pi pii1 (t1 ) pi1i2 (t 2 t1 )

, X (t n )= in} pin 1in (t n t n 1 )