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Continuous-time nonlinear stochastic differential state and measurement equations, all of which have coefficients capable of abrupt changes at a random time, are considered; finite-state jump Markov chains are used to model the changes. Conditional probability densities, which are essential in obtaining filtered estimates for these hybrid systems, are then derived. They are governed by a coupled system of stochastic partial differential equations. When the Q matrix of the Markov chain is eitherdoi:10.1109/9.802937 fatcat:lo6xradrzrb3raohkbvd5ylzdm