Evaluation formulas for generalized conditional wiener integrals with drift on a function space

Let c[0,t] denote a generalized wiener space,the space of real-valued continuous functions on the interval [0,t] and define a stochastic process y:c[0,t]×[0,t]→r by y(x,s)=∫0szh(u)dx(u)+a(s) for xεc[0,t] and se[0,t],where hel2[0,t] with h≠0 a.e. and a is continuous on [0,t]. let random vectors yn:c[0,t]→rn and yn+1:c[0,t]→rn+1 be given by yn(x)=(y(x,t1),.,y(x,tn)) and yn+1(x)=(y(x,t1),.,y(x,tn),y(x,tn+1)),where 0