Filtering of Finite-State Time-Nonhomogeneous Markov Processes, a Direct Approach

A filtering equation is derived for P(x _t =x|y _s ,s∈[0,t]) for a continuous-time finite-state two-component time-nonhomogeneous cadlag Markov process z _t =(x _t ,y _t ) . The derivation is based on some new ideas in the filtering theory and does not require any knowledge of stochastic integration. Accepted 10 August 1999. Online publication 13 November 2000.