Before revision: Furthermore, it is a general fact about conditional expectations that if F is any sub-σ-algebra of Σ then the orthogonal projection is exactly the conditional expectation operator E[·|F], i.e., Hence, This elementary result is the basis for the general Fujisaki-Kallianpur-Kunita equation of filtering theory
After revision: .Furthermore, it is a general fact about conditional expectations that if F is any sub-σ-algebra of Σ then the orthogonal projection is exactly the conditional expectation operator E[·|F], i.e., Hence, This elementary result is the basis for the general Fujisaki-Kallianpur-Kunita equation of filtering theory