OK, that was annoying... one more time:
> I'm a professor
[insert retort about ivory-tower academics HERE]
> You seem very sure that Caesar existed and that he 'wrote his own stuff.' I just want you to back it up historically.
It can be backed up through inductive reasoning. Caesar's existence is not known from a single source, but from a wide variety of sources all dating from the same era, and largely agreeing. This is not the case for Christ. Many of the early reports of Christ are ignored as they are heretical. If you tell me that you ate toast for breakfast this morning, it does not take me much to believe. if you tell me you had refried Velociraptor for breakfast, I will need rather more evidence. Similarly, you tell me that there was once a brilliant military leader who gained political power, that's not terribly exceptional. Tell me about someone who coudl walk on water, materialize food, raise the dead and tinker with peoples souls, I'll want rather more than your say-so. And when your say-so is as inconsistant as the Gospels... well, you've got some 'splainin' to do.
So far, you haven't provided anything but your own opinions.
If you are going to say that Caesar wrote 'his own stuff' and is an historical figure, the responsibility is yours to back it up with data.
The book of Mark is agreed by biblical scholars, (and we are talking, say, Oxford here, among others) to be Peter's eyewitness account as written down by Mark. Luke was a contemporary of Peter and Paul, as well as the other apostles, and is the author of Luke, as well as the Acts of the Apostles. Mark and Luke were scribes, a common occupation in those days, and were men who often accompanied remarkable teachers and wrote down their teachings and the accounts of their lives. Paul himself was a learned learned Torah scholar who came to see that Jesus was the fulfilment of the Torah prophecies. The account of "walking on water", turning water into wine, performing miracles, etc. served a deeper purpose in teaching that was known to students of the OT.
Josephus, Hillel, Hebrew scribes and a few other Gentile historians do make references to Jesus, proving that He did walk the earth, at that time.