Parallel computations for Yau filters

In the early 1990s, Yau developed a new class of nonlinear filters, called the Yau Filterswhich contain the Kalman-Bucy filters and the Benes filters as special cases. It has been shown that, from the Lie algebraic point of view, the Yau filters are the most general finite-dimensional filters. Yau and Hu proved that the DMZ equation for a Yau filter can be reduced to a Kolmogorov type partial differential equation and a system of linear differential equations. They noticed that the PDE is independent of the observed data and hence can be solved off-line. An efficient parallel algorithm for the system of ODEs would lead to fast solutions of Yau filters and hence their suitability for real-life applications. In this paper, we have proposed several parallel methods suitable for this system of ODEs.