# A stochastic model for extinction and recurrence of by Finkenstadt B. F. By Finkenstadt B. F. By Finkenstadt B. F.

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Additional resources for A stochastic model for extinction and recurrence of epidemics estimation and inference for measles o

Example text

He r e m a i n i n g 'local' index-set r e c u r s i o n s can be obtained in a similar w a y . 46 T h e s e recursLons, together with the corresponding index-set section are presented in Appendix I. ssociated with the {x,x+n+l} ) is arriving to the s c h e m e of Fig. 1 al: the 'global' order-updaLe step n + n+l. T h e 'local' structure of this order- update step is presented in 5"[g. Z. __> Lx~n _ ~ .... n+l,n-i ~ Lx,n÷l n+l,n+2 Ln+ I,n+ l Lx,n + n+l,n Lnx'+~,n+1 Lx,n-I n,n+ I Lx,n-I n+ l,n-I Lx, n-i n+ l,n LXP 0 n,2 LX, O n+l,o LX, O n,n+l f X~O f - .

F r o m ( 2 . 3 ~ a ) , ( a . 48a) m_ re@u_ ~'N" 2. 46eL) M (MeN Z ~ViVN) - . ,,%) z]c=e ~ M M N T T ... e N ~ j1=l ... ••pm N ~ ... Id u e M ---e N j m-Jm_i i8r N ~ kl--i ... Jmkl---ku . k u M M 2 r m = l u=1 mF. N" (M}F,N {M×M} • -, This proves m • u.. 49b) ( 2°~7d). I stochastic estlma£ion problem considered in the space X N _ l , c ~ be equivalently interpreted ~s the deterministic problem in the space { M } KI~-_ 35 of ~eneralized matrices, or as the de£ermlrdst/c p r o b l e m in the s p a c e {M}_IzN_I of generaJ/zed z-polynomieds.

Q:nl -- ) lq)O so that we will define -1 ~x,n n,o The n,o A x,n-1 = P~;n-l,n L-backward k p x,n-i = R;n-l,n i x + n L-backward B x,n-1 the approximation lx+n = - ix+n} estimate (3,19a) as l[x,n-i n-l,n e error :1. x+n ! 21a) x~n . xln--I Kntn+l , v [in~ n , ix,x+n } , m=n+l (3 21b) " the B - b a c k w a r d ~x,n-1 n,m ~= _ x,n-I P~;n,m-i ix, n A= P x,n-i n, n+ 1 ]I;n,n Consequently, estimates will be e x p r e s s e d C B x,n nmn+l IIx'n-I n,m-i , ix, x+ n Nx'n-1 n, n ' the B - b a c k w a r d c approxima£ion ;n,m-I i x + n + l-m,x+n A= Pli x,n-1 ;n,n as i x + n + l-m,x+n i x,x+n ± !