Dimensional reduction in nonlinear filtering: A homogenization approach
Peter Imkeller, Navaratnam Sri Namachchivaya, Nicolas Perkowski, Hoong, C. Yeong · 2012
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 $\sqrt{\varepsilon}$. 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.