Game of Thrones Jon Snow family (supposition)

I've been on this thought since I read the first book and watched the first season, and the feeling behind the thought keeps getting more certain, or probable, since the book series is still being written and the TV series doesn't have to match it exactly, but has been closer than TRUE BLOOD / SOOKIE STACKHOUSE SERIES.

My supposition is this:

GoT Bastard and warg Jon Snow is not Eddard / Ned Stark's son but his stepson and nephew by blood, being his sister, the secret warg, Lady Lyanna Stark's child by Crown Prince RhaegarTargaryen or soon to be King Robert Baratheon.

Book VI not yet available.