Nonlinear filtering of reflecting diffusion processes (Q919705)

In the nonlinear filtering model \(y_ t=h_ t(X_ t)+e_ t\), \(0\leq t\leq T\), where \((e_ t)\) is a finitely additive white noise, the problem of finding the conditional density u(t,x) of \(X_ t\) given observations \(\{y_ u:\) \(0\leq u\leq t\}\) is considered when \((X_ t)\) 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.