  We provide here global Schauder-type estimates for a chain of integro-partial
differential equations (IPDE) driven by a degenerate stable Ornstein-Uhlenbeck
operator possibly perturbed by a deterministic drift, when the coefficients lie
in some suitable anisotropic H{\"o}lder spaces. Our approach mainly relies on a
perturbative method based on forward parametrix expansions and, due to the low
regularizing properties on the degenerate variables and to some integrability
constraints linked to the stability index, it also exploits duality results
between appropriate Besov Spaces. In particular, our method also applies in
some super-critical cases. Thanks to these estimates, we show in addition the
well-posedness of the considered IPDE in a suitable functional space.
