  We develop a theory of Anosov representation of geometrically finite Fuchsian
groups in SL(d,R) and show that cusped Hitchin representations are Borel Anosov
in this sense. We establish analogues of many properties of traditional Anosov
representations. In particular, we show that our Anosov representations are
stable under type-preserving deformations and that their limit maps vary
analytically. We also observe that our Anosov representations fit into the
previous frameworks of relatively Anosov and relatively dominated
representations developed by Kapovich-Leeb and Zhu.
