EXCHANGEABLE MARKOV PROCESSES ON [k]N WITH CADLAG SAMPLE PATHS

Any exchangeable, time-homogeneous Markov processes on [k] with cadlag sample paths projects to a Markov process on the simplex whose sample paths are cadlag and of locally bounded variation. Furthermore, any such process has a de Finetti-type description as a mixture of independent, identically distributed copies of time-inhomogeneous Markov processes on [k]. In the Feller case, these time-inhomogeneous Markov processes have a relatively simple structure; however, in the nonFeller case a greater variety of behaviors is possible since the transition law of the underlying Markov process on [k] can depend in a non-trivial way on its exchangeable σ-algebra.