同理，当n≥1时，有 液 Pn(t+h)=P(N(t+h)=n) =P(N(t)=n,N(t+h)-N(t)=0) +P(N(t)=n-1,N(t+h)-N(t)=1) +P(N(t+h)=n,N(t+h)-N(t)=2) =Pn(t)Po(h)+Pn-1(t).Pi(h)+o(h) 11/47 =(1-Xh)Pn(t)+XhPn-1(t)+o(h). 于是 Pn.(t+h)-Pn(t) h =-入Pn(t)+λPn-1(t)+o(h), 令h→0得 P(t)=-λPn(t)+入Pn-1(t) GoBack FullScreen Close Quit11/47 kJ Ik J I GoBack FullScreen Close Quit ”nßn ≥ 1ûßk Pn(t + h) = P(N(t + h) = n) = P(N(t) = n, N(t + h) − N(t) = 0) +P(N(t) = n − 1, N(t + h) − N(t) = 1) +P(N(t + h) = n, N(t + h) − N(t) ≥ 2) = Pn(t)P0(h) + Pn−1(t) · P1(h) + o(h) = (1 − λh)Pn(t) + λhPn−1(t) + o(h). u¥ Pn(t + h) − Pn(t) h = −λPn(t) + λPn−1(t) + o(h), -h → 0 P 0 n (t) = −λPn(t) + λPn−1(t)