Applying the EKF to stochastic differential equations with level effects

A transformation is introduced to effectively remove level effects, i.e. the state dependency of the diffusion function, in a restricted class of multivariate stochastic differential equations such that the general continuous–discrete-time nonlinear filtering problem may be solved using new or existing implementations of the extended kalman filter (EKF).

An implementation of a quasi-maximum likelihood (QML) method for direct estimation of embedded parameters in nonlinear, multivariate stochastic differential equations using discrete-time input–output data encumbered with additive measurement noise is discussed, and its properties are compared with those provided by another software package.