Dimensional reduction in nonlinear filtering: A homogenization approach

Abstract

We propose a homogenized filter for multiscale signals, which allows us to reduce the dimension of the system.We prove that the nonlinear filter converges to our homogenized filter with rate √ ε. This is achieved by a suitable asymptotic expansion of the dual of the Zakai equation, and by probabilistically representing the correction terms with the help of BDSDEs. © Institute of Mathematical Statistics, 2013.