第4章-更新过程.pdf

1/53kJIkJIGoBackFullScreenCloseQuitAAALLL?IIIOOO?2/53kJIkJIGoBackFullScreenCloseQuit1114#LLL 4.1#L9eZ 4.2#9A 4.3#n 4.4#L?23/53kJIkJIGoBackFullScreenCloseQuit4.1#LLL999eeeZZZ 4.1.1?Xn,n=1,2,G?KC,F(x)(?;?F(0)=P(Xn=0)6=1P=EXn=R0 xdF(x),K0 ).-Tn=Pni=1Xi(n 1),T0=0.rdN(t)=supn:Tn t?OL#LLL.#L?;.f?.30SC#m$1?d3X1#?5O(bOIm)K1?3X1m$1?3X2?1n4/53kJIkJIGoBackFullScreenCloseQuit.g,?o?t?8?#L.53#Lu)g?g#Xn1n 1g1ng#?m Tn1ng#u)?N(t)tcu)?o?#g.4.1.1N(t)?999EN(t)?555N(t)0,?n Tn,5/53kJIkJIGoBackFullScreenCloseQuitg#U3?mSu).ukmSUu)kg#.N(t)n Tn tP(N(t)=n)=P(N(t)n)P(N(t)n+1)=P(Tn t)P(Tn+1 t)=P(nXi=1Xi t)P(n+1Xi=1Xi t)FnPTn?KFnF?n-dP(N(t)=n)=Fn(t)Fn+1(t)6/53kJIkJIGoBackFullScreenCloseQuitnnn 4.1.1M(t)=Xn=1Fn(t)M(t)=EN(t),#.yyy d?M(t)=EN(t)=Xn=1nP(N(t)=n)=Xn=1nFn(t)Fn+1(t)=Xn=1Fn(t)7/53kJIkJIGoBackFullScreenCloseQuitnnn 4.1.2 M(t)t?0 t +,M(t)+.yyy duN(t)ut?M(t)?eyM(t)?k5.db?F(0)1,=P(Xn=0)0)0)K3a 0,?P(Xn a)0,l?P(Xna)1.?F(a)=P(Xn a)=P(Xn a)+P(Xn=a)?;P(Xn=a)=P(Xn a)EF(a)=P(Xna)+P(Xn a)=1?”?0 b a F(b)P(Xn a)b,X2 b,Xk bcuP(Tk t)1 P(X1 b,X2 b,Xk b)=1 1 F(b)k=1 p=(1 F(b)k 0.qTmk t TkT0 t,T2kTk t,TmkT(m1)k t#m,kP(Tk T0 t,T2k Tk t,Tmk T(m1)k t)=P(Tk t)m9/53kJIkJIGoBackFullScreenCloseQuitd?P(Tmk t)P(Tk t)m(1 )m?j 0kTmk+j t Tmk t(m+1)k1Xn=mkP(Tn t)kP(Tmk t).10/53kJIkJIGoBackFullScreenCloseQuitn?M(t)=Pn=1Fn(t)=Pn=1P(Tnt)=Pk1n=1P(Tnt)+Pn=kP(Tnt)Pk1n=1P(Tnt)+Pm=1kP(Tmkt)Pk1n=1P(Tnt)+Pm=1k(1)m=Pk1n=1P(Tnt)+k?m(t)=Xn=1fn(t)fn(t)Fn(t)?.nnn 4.2.1 M(t)m(t)OvM(t)=F(t)+Zt0M(t s)dF(s)m(t)=f(t)+Zt0m(t s)f(s)ds14/53kJIkJIGoBackFullScreenCloseQuitf(t)=F0(t).yyy ky1d?M(t)=Xn=1Fn(t)=F(t)+Xn=2Fn(t)=F(t)+Xn=2Fn1 F!(t)=F(t)+Xn=1Fn F!(t)=F(t)+(M F)(t)d(M F)(t)=Rt0M(ts)dF(s)l?1?y.1?d1?.4.2.2(#)Xe/?15/53kJIkJIGoBackFullScreenCloseQuit#K(t)=H(t)+Zt0K(t s)dF(s)H(t),F(t)?t 0ksup0tT|K(t)|H(t)|+ZT0sup0sT|H(T s)|dM(s)sup0tT|H(t)|(1+M(T)17/53kJIkJIGoBackFullScreenCloseQuit3k.mK(t)k.?.25wv#.d1 kK(t)=H(t)+M H(t)=H(t)+(F+F M)H(t)=H(t)+F (H+M H)(t)=H(t)+F K(t)?y5Iy#?)k1?/.?K(t)#?)vk.5KdK(t)=H+F K(t)Y“K(t),k18/53kJIkJIGoBackFullScreenCloseQuitK=H(t)+F (H+F K)(t)=H(t)+F H(t)+F (F K)(t)=H(t)+F H(t)+F2K(t)=H(t)+F H(t)+F2(H+F K)(t)=H(t)+F H(t)+F2 H(t)+F3K(t)=H+n1Xk=1Fk!H+FnK(t).5?t,|FnK(t)|=|Zt0K(t x)dFn(x)|sup0 xt|K(t x)|Fn(t)19/53kJIkJIGoBackFullScreenCloseQuitdbsup0 xt|K(tx)|,M(t)=Pn=1Fn(t),limnFn(t)=0,tl?limn|FnK(t)|=0.?limn n1Xk=1Fk H(t)!=Xk=1Fk!H(t)=M H(t)uK(t)=H(t)+limnn1Xk=1Fk H(t)+FnK(t)#=H(t)+M H(t),20/53kJIkJIGoBackFullScreenCloseQuit1.4.2.1(Wald?)?EXi tx+E(TN(tx)+1),e x tX4-1.21/53kJIkJIGoBackFullScreenCloseQuitPK(t)=E(TN(t+1),KK(t)=ETN(t)+1=E?E(TN(t)+1|X1=x)?=Z0E(TN(t)+1|X1=x)dF(x)=Zt0 x+K(t x)dF(x)+ZtxdF(x)=EX1+Zt0K(t x)dF(x)#d#)35n,K(t)=EX1+Zt0EX1dM(x)=E(X1)(1+M(t)=E(X1)(EN(t)+1).555 p?Wald?y=?#22/53kJIkJIGoBackFullScreenCloseQuitn?A|5?y.ETN(t)+1=Xk=0EN(t)+1Xi=1Xi|N(t)=kPN(t)=k=Xk=0Ek+1Xi=1XiPN(t)=k=Xk=0(k+1)EX1PN(t)=k=EX1kXk=0PN(t)=k+Xk=0PN(t)=k=EX1EN(t)+123/53kJIkJIGoBackFullScreenCloseQuit4.2.2#333?AAA(5?0)db)S(x)(#)?U?c#x?V9)?c#r(x)(x 0)(c#x?1)?=(x)dt13dt?mmS)e?).3t,kB(tx)S(x)dx5?c#3x?x+dxm,xcc)?xc?1)?B(t)CeRt,t ()?L),CRvZ0eRyS(y)(y)dy=1=)9kd?+CO.eF()0,B(t)C/u0+?k?F()=1,)uk?.26/53kJIkJIGoBackFullScreenCloseQuit4.3#nnn313?r?PoissonL?gu)?mmXnl?#M(t)=EN(t)=t,uM(t)t=1EXn(4.3.1)ou?#Lk5Qnnn 4.3.1(Feller?#n)P=EXnKM(t)t1(t ),e=,1=0.yyy kb?t27/53kJIkJIGoBackFullScreenCloseQuit?,|4.2.1?(,?M(t)+1 t=M(t)t11tl?liminftM(t)t1.,?M,-Xcn=(Xn,Xn MM,Xn M28/53kJIkJIGoBackFullScreenCloseQuitKXcn,n=1,2,(?#?#L.-Tcn=nXi=1XciN(t)c=supn:Tcn tduXcn M,KTcNc(t)+1 t+M2|4.2.1,?M(t)c+1 M t+MM=E(Xcn),M(t)c=EN(t)c,d?M(t)ct+M1M1t+Ml?limsuptM(t)ct1M29/53kJIkJIGoBackFullScreenCloseQuitq Xcn Xn,?Tcn Tn,N(t)c N(t),M(t)cM(t).ulimsuptM(t)t1M-M ,kXcn Xn,E(Xcn)EXn,=M limsuptM(t)t1|?n(.?=,2dXcn(?L.?M ,.d(.n?w?t M(t)30/53kJIkJIGoBackFullScreenCloseQuitt.g,?t ,u?hkM(t+h)M(t)h(=t+ht)(4.3.2)d,?,-?#nBlackwell#n.?nk#?Vg.4.3.1(:)e3d 0,?Xn=0P(X=nd)=1CXl:(CX?F:)v?dd:?.555 lU?:3d?V0?knd(n=0,1,2,)?.31/53kJIkJIGoBackFullScreenCloseQuitnnn 4.3.2(Blackwell#n)P=EXn1eF:Ka 0,?t ,M(t+a)M(t)a.2eF:d,K?n ,P(3nd?u)#)d.555 Blackwelln,3?l?:?,a?mS#g?a,*Nn)?1?5wm?#Lu)?(SK4.3).?F:du#Uu)3d?,(1)U?#g?6um/Xnd?:?8?mSkda:?8?.32/53kJIkJIGoBackFullScreenCloseQuit?#nBlackwelln?A/.,-bn=Mn Mn1,?F:,d(1)bn1,n d4?5?b1+b2+bnn=M(n)n1,n?t,ttM(t)tM(t)tt+1tM(t+1)t+1ptLt?,=Lt?.-t?M(t)t1Fellern.?F:gCy.33/53kJIkJIGoBackFullScreenCloseQuitnnn 4.3.3(#n)P=EXn,?h(t),t 0,),vih(t)KO;(ii)R0h(t)dt .H(t)#H(t)=h(t)+Zt0H(t x)dF(x)?).o1eF:,klimtH(t)=(1R0h(x)dx,0,=2eF:u0 c d,klimnH(c+nd)=(dPn=0h(c+nd),0,=#nBlackwelln?d5:F:?3#n?v(i),(ii)34/53kJIkJIGoBackFullScreenCloseQuit?h(t)=(1,0 t 0,limtM(t+a)M(t)a=1?lima0limtM(t+a)M(t)a=1.b?4gS?,klimtdM(t)dt=1=?t,kdM(t)1dt qR0h(x)dx?Xi(i=1,2,)l45?”?I?+?+?#?m Yi(i=1,2,)l0.5?!.m?.)N(t)L?t?g#mEXi+Yi=45.5?.?limtM(t)t=145.5=291(g/?)4.3.2?k?1?w?Poisson?z?mC1.?U3?sO?5.37/53kJIkJIGoBackFullScreenCloseQuit(1)?1?(2)?m?.)?mmXiuEXi=1(i=1,2,);?mYilEYi=1(i=1,2,).(1)?1?m1+1=+?1?+.(2)?m1/1+1=+.4.3.3 lm?#LN(n),n=0,1,2,3zm:/Bernoulli?Vp”?Vq=1 p?#M(n)PdL?#limnM(n)n.)?g?mmXi?PXi=38/53kJIkJIGoBackFullScreenCloseQuitk=pqk1,k=1,2,#mEXi=+Xk=1kpqk1=p+Xk=1(qk)0=p+Xk=1qk!0=p(q1 q)0=1p?klimnM(n)n=1EX1=p 4.3.4,?gl1g?PoissonLmY1,Y2,pl?CS?v EY1?5N(t)L?t5?gylimnEN(t)t=1+EY139/53kJIkJIGoBackFullScreenCloseQuit)(?S?#L.eXiL1i 1g(?1ig?5?mmK#?mmXi+Yi#m=EXi+Yi=1+EY1l?limnEN(t)t=1+EY1 4.3.5 c#?4 r(t)=TN(t)+1tLt?=l t m?eg#?m,s(t)=t TN(t)t?c#.r(t)s(t)?4.):-Ry=P(r(t)y)40/53kJIkJIGoBackFullScreenCloseQuit1g#?X1?,?P(r(t)y|X1=x)=1,x t+y0,t x t+yRy(t x),0 y|X1=x)dF(x)=Zt+ydF(x)+Zt0Ry(t x)dF(x)=1 F(t+y)+Zt0Ry(t x)dF(x)#.?)Ry(t)=1 F(t+y)+Zt01 F(t+y x)dM(x)41/53kJIkJIGoBackFullScreenCloseQuitEb?=EX1,K=Z0 xdF(x)=Z01 F(x)dx Z01 F(t+y)dt=Zy1 F(z)dz y)=limtRy(t)=1Zy(1 F(z)dz,z 0c#s(t)?d?.5?r(t)x,s(t)y r(t y)x+y42/53kJIkJIGoBackFullScreenCloseQuitl?limtP(r(t)x,s(t)y)=limtP(r(t y)x+y)=1Zx+y1 F(z)dzAO/limtP(s(t)y)=limtP(s(t)y,r(t)0)=1Zy1 F(z)dz.5551 3A#n?E|ku,g#(1gtc?g)?#2|#n.5552?c#?443/53kJIkJIGoBackFullScreenCloseQuit?Xn)(44/53kJIkJIGoBackFullScreenCloseQuit4.4#LLL?2224.4.1#LLL#LmmX1,X2,F?S?.XJX1?#NlO?GKdX1,X2,(?OL#LLL.X34.1!?fb?m*?1$1?mK?mX1A#U?mX2,X3,.?5?X1,X2,m?5E,7I?.yu#L4.3!?n#n,(5 M(t)=Pn=1Fn(t)?Fn(t)AF1(t)=G(t),Fn(t)=G Fn1(t)(n 2)5O45/53kJIkJIGoBackFullScreenCloseQuit?(XF1 G,F2 G F,F3 G F F,?).*?w,?1g#u)?k?K.4.4.1#LmmX1,X2,F?S?.XJX1?#NlO?G,KdX1,X2,(?OL#LLL.4.4.2#?LLL 4.4.2?R(t)=N(t)Xi=1RiN(t),t 0#L,Rn,n=1,2,46/53kJIkJIGoBackFullScreenCloseQuitN(t),t 0,KR(t)#?LLL555 dur Rnw1ng#u)?.?#?L#NRn6uXn(=?mk)?(Xn,Rn).nnn 4.4.1#?ne#mX1,X2,vEX1,zg?RnvER1.K(1)limt1tR(t)=ER1EX1w.p.1;47/53kJIkJIGoBackFullScreenCloseQuit(2)limt1tER(t)=ER1EX1.4.4.1?,i?Xe:e?,3wS,K?.e3(w,w+Tm,KUmd#?.3(0,w S?#?1?5?,?3(w,w+TSd?#?,l-#O.?1d?K=?|d?,b?,?!?#?.)?t=0r?#?,dc,?c0c,?X,?F(t),EX=wym,dY1?,Y1=w+Rw(Rw?3w?),Y1=TN(w)+1,X4-3.49/53kJIkJIGoBackFullScreenCloseQuitl?G(t)=P(Y1 t)=(1,0 t wP(w+Rwt)=F(t)+Rw0F(tx)dM(x),w w+Tc(Y1w)T,w x)dx50/53kJIkJIGoBackFullScreenCloseQuituc(w,T)=Ec1EY1=cRT0P(Rw x)dxT1+M(w)i?|drG?3(0,wmS?EN(w)=M(w).d3?(0,Y1S,iG?c0M(w)+1ilzr?|dc(w,T)c01+M(w)1+M(w)=c(w,T)c0.4.4.3?OOO#LLL 4.4.3 3#LXkG?,Xm?=Im.?S?k?L51/53kJIkJIGoBackFullScreenCloseQuitm“0?.p5k“m0“0G?#L,L?OOO#LLL.5551?Xm?Ym?mZ1?4,mY1,?2mmZ2,q4,mY2,?O?1,z?X?mg#.5552 b?(Zn,Yn),n=1,2,.?l?Zn,Yn?=Zi,Yj3i 6=j?Zi,Yi#N.nnn 4.4.2?HZn?GYn?FZn+Yn?.P P(t)=P(tXm?)?E(Yn+Zn)t|Z1+Y1 t),x tP(t x),x t)+Zt0P(t x)dF(x)=H(t)+Zt0P(t x)dF(x)?)P(t)=H(t)+Zt0H(t x)dM(x)53/53kJIkJIGoBackFullScreenCloseQuitqR0H(t)dt=EZ1 w,H(t)KOd#n?limtP(t)=R0H(t)dtE(Y1+Z1)=EZ1EZ1+EY1