Publications and Preprints

We consider the nonlinear filtering model with Ornstein-Uhlenbeck process as noise and obtain an analogue of the Bayes’ formula for the filter. For this we need to consider a modified model, where the instaneteneous effect $h(X_t)$ of the signal in the usual model is replaced by $\xi_t^\alpha = \alpha \int_{(t-\frac{1}{\alpha}) \vee 0}^t h(X_u) du$, (where $\alpha$ is a large parameter). This means that there is a lingering effect of the signal for a time period $\frac{1}{\alpha}$. Further, we also show the filter with Ornstein-Uhlenbeck converges to the usual filter in probability.