a第8讲第3章 泊松过程2.pdf

[0, t) λ 2.5 / 15 10 210 5 3 1 2 3.2 { } X (t ), t ≥0 λ 0 1X (0) 0 2X (t ) 3t A λt 0 { } P X t + − ( ) ( ) s X s n 3.3 1X (0) 0 −λt (λt )n e ,n 0,1, L 2X (t ) n! 3X (t ) { } P X (t +h) −X (t ) 1 λh +o(h) { } P X (t +h) −X (t ) ≥2 o(h) 3 m (t ) E [X (t )] λt , 2 X σ (t ) D [X (t )] λt X RX (s, t ) E [X (s)X (t )] λs(λt +1), (s t ) BX (s, t ) λmin(s, t ), gX (u) E [eiuX (t ) ] exp[λt (eiu −1)] 4