>Stoicism was influenced by Skepticism

No, not much at all. Stoic epistemology was overall very positive and much adverse to Skeptic arguments. The debates of Stoics during the centuries after Zeno of Citium, the founder, were mostly directed against the Middle Platonists of the so-called Skeptic Academy, who were those that actually were very influenced by the Skeptics. In fact, this skeptic alignment of the Platonists allowed the Stoics to revisit Plato and make more and more use of him, i.e. there was a Platonizing effect on the Stoa's teachings during this time. Originally, Stoicism had its roots in the teachings of the Cynic and Platonic schools along with a good helping of the Dialecticians (Megarians) and Stilpo (a 'free lancing' 'Socratic', and one of Zeno's teachers).