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. When a model is specified by given risk-neutral probabilities together with a given short rate function of the Markovian driver , we give three sufficient conditions for existence of a recurrent eigenfunction (and , hence, of a recurrent Hansen-Scheinkman factorization and Ross recovery)
After 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 BRPs, and obtain the long maturity asymptotics of the pricing operator. When an asset pricing model is specified by given risk-neutral probabilities together with a given short rate function of the Markovian driver , we give three sufficient conditions for existence of a recurrent eigenfunction (and , hence, of a recurrent Hansen-Scheinkman factorization and Ross recovery)