Sequential estimation of diffusion processes

The paper considers the sequential estimation problem for the unobservable component $\theta_t$ of a two-dimensional diffusion process $(\xi_t,\theta^t)$ satisfying (1) from the data $\xi_0^T$. By a method different to that of [1], [6], equations of optimal filtering and (forward) interpolation (Theorems 6 and 7) are obtained under essentially weaker conditions.