Special solutions to some Kolmogorov equations arising from cubic sensor problems
Ruxu Du, Lixing Jia, Stephen S.‐T. Yau · Communications in Information and Systems · 2007
1. Introduction. Ever since the technique of the Kalman-Bucy filter was pop-ularized, there has been an intense interest in developing nonlinear filtering theory. Basically we have a signal or state process x = {xt} which is usually not observable. What we can observe is a related process y = {yt}. The goal of nonlinear filtering is to determine the conditional expectation of the form E[φ(xt) : ys, 0 ≤ s ≤ t] where φ is