5.1连续时间马尔可夫链
例5.1证明泊松过程{X(t), t≥0}为连续时间齐次马尔可夫链。证明：先证泊松过程的马尔可夫性。证明：泊松过程是独立增量过程，且X(0)=0,对任意0<t1< t2<…< tn< tn+1有P{ X (t n+1 )= in+1| X (t1 )= i1, X (t 2 ) X (t1 )= i2 i1,, X (t n )= in}= P{ X (t n+1 ) X (t n )= in+1 in| X (t1 ) X (0)= i1,, X (t n ) X (t n 1 )= in in 1}= P{ X (t n+1 ) X (t n )= in+1 in}