Nonlinear filtering of reflecting diffusion processes

In the nonlinear filtering model yt=ht(Xt)+et, 0[less-than-or-equals, slant]t[less-than-or-equals, slant]T, where (e1) is a finitely additive white noise, the problem of finding the conditional density u(t,x) of Xt given observations {yu:0[less-than-or-equals, slant]u[less-than-or-equals, slant]t} is considered when (Xt) is a reflecting diffusion process. It is shown that u(t,x) can be obtained as the unique classical solution of an initial-boundary value problem for a parabolic PDE.