Applying the EKF to stochastic differential equations with level effects

A transformation is introduced to e!ectively remove level e!ects, i.e. the state dependency of the di!usion function, in a restricted class of multivariate stochastic di!erential equations such that the general continuous}discrete-time nonlinear "ltering problem may be solved using new or existing implementations of the extended kalman "lter (EKF). An implementation of a quasi-maximum likelihood (QML) method for direct estimation of embedded parameters in nonlinear, multivariate stochastic di!erential 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. ( 2000 Elsevier Science Ltd. All rights reserved.