Before revision:  As an application , we prove uniqueness of the Hansen and Scheinkman (2009) factorization of the Markovian pricing kernel under the assumption of recurrence, and, as a special case, we extend the Recovery Theorem of Ross (2013) from discrete time, finite state irreducible Markov chains to recurrent Borel right processes.
After revision:  As an application , we prove uniqueness of the Hansen and Scheinkman (2009) factorization of the Markovian SDF corresponding to the recurrent eigenfunction, extend the Recovery Theorem of Ross (2013) from discrete time, finite state irreducible Markov chains to recurrent Borel right processes.