Linear filtering in multiplicative noise

Linear filtering of a continuous dynamical system is considered where the noise appears multiplicatively. It is first shown that the solution process is a log normal process. The estimator equation and the variance equation for the filter are then derived, which are shown to be coupled. A successive approximation scheme is proposed whereby at each iteration step the estimator equation and the variance equation are separable and take forms similar to that of the Kalman-Bucy filter for the additive-noise case.