Incidentally, I have a copy of Loeve's old probability textbook - I wonder if it is too out of date to be any use.
Basically we're talking graduate probability based heavily on measure theory and some on functional analysis.
Last I heard of Neveu he was back in France and at least in part working on probability for stock markets.
There are other more recent authors. It seems that a big fraction of the best researchers sometimes take out a year and write yet another book comparable with Neveu. Personally, I did enough with Loeve, Neveu, Breiman, and Chung and for more attention to such material want to use that background to move on. For now, I'm concentrating on my startup; it's based one some applied math I derived, but I've done that and programmed it. Tonight I got four hard disks installed in my first server. Three of them are partitioned and formatted, and as I type this the fourth is being partitioned and formatted.