Filtering with a limiter

Abstract

We consider a filtering problem for a Gaussian diffusion process observed via discrete‐time samples corrupted by a non‐Gaussian white noise. Combining the Goggin′s result [2] on weak convergence for conditional expectation with diffusion approximation when a sampling step goes to zero we construct an asymptotic optimal filter. Our filter uses centered observations passed through a limiter. Being asymptotically equivalent to a similar filter without centering, it yields a better filtering accuracy in a prelimit case.