Theoretical Statistics and Mathematics Unit, ISI Delhi

On Filtering with Ornstein-Uhlenbeck Process as Noise

by Abhay G. Bhatt and Rajeeva L. Karandikar

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.

isid/ms/2002/32 [fulltext]

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