Before revision:  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) for specific classes of Markovian models and provide explicit examples of recurrent eigenfunctions, recurrent Hansen-Scheikman factorizations, and Ross recoveries in a number of  models, including affine and quadratic diffusion models , some non-affine diffusion models, and an affine model with jumps.
After revision:  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 provide explicit examples of recurrent eigenfunctions, recurrent Hansen-Scheikman factorizations, and Ross recoveries in a number of models, including affine and quadratic diffusion models , some non-affine diffusion models, and an affine model with jumps.