Naive question: Origin of the Holy Ghost

I have heard that there is a lot of influence from the Greeks in the development of Christianity, the Stoics and Platonists, and the concept of *logos*, the Word, and Jesus. You can see this in the Gospels, the book of Enoch, Daniel, etc. This, as far as I know, is an established fact of modern biblical scholarship (not from a religious but an academic point of view), But where does the Holy Ghost fit into this Greek influence and what is he (they?) supposed to be? Sorry if this is a dumb question, but does the Holy Ghost come from Greek influence? Are they the ghost of a dead Jesus? How does that make sense if Jesus was said to be resurrected? What is the origin, as far as scholarship can tell (textual analysis, archeology, etc.), of the Holy Ghost and what is their nature and relationship to the other two?