For a class of partially observed Markov processes a representation for the optimal non-linear filter is obtained in which stochastic integrals are absent.Let , / = (0, 0 = (Ot,~t), 0 < t < T, be a partially observable M a r k o v process on some probability space (f], ~, P ) , satisfying the following system of stochastic differential equations
dOt=[ao(t,t;t)+al(t,t;t)St]dt+bl(t,~t)dWl(t)+b2(t,~t)dw2(t),(1)
d~t--[Ao(tl,~t)+ Al(t,~,)Ot]dt+ B(t,~t)dw2(t ),where w 1 ---(Wl(t), ~t), W2 ~-(w2(t), ~t) are independent Wiener processes, (~t), 0 < t < T, is a non-decreasing family of o-subalgebras of ~.Let coefficients ai (t,x ), Ai(t,x ),1,bi(t,x ), i= 1,2,B(t,x)
f0 ( / (lai(t,x)l+lhi(t,x)l}+ ~. bfl(t,x)+ n2(t,x) dt< oo;i ~ 0,1 j~ 1,22) for each x ~ R 1 for[ 2
Ao(t,x)+A2(t,x)]dtO,