Nonlinear filtering is a central mathematical tool in understanding how we process information. Unfortunately, the equations involved are often high dimensional, and therefore, in practical applications, approximate filters are often employed in place of the optimal filter. The error introduced by using these approximations is generally poorly understood. In this talk we will see how, in the case where the underlying process is a continuous-time, finite-state Markov Chain, results on the stability of filters can be strengthened to yield bounds for the error between the optimal filter and a general approximate filter. We will then consider the 'projection filter', a low dimensional approximation of the filtering equation originally due to D. Brigo and collaborators, and show that its error is indeed well-controlled. The talk is based on joint work with Sam Cohen.
