Recently I've become fixated on random processes, could you reccomend any books that can be understood with multivariable analysis knowledge? I wanna know how deep this rabbithole goes.

It is to my understanding that this stuff is relatively new in comparison to other fields of mathematics, most work on iterative functions was done in the 70s (even though Julia sets and fractals were discovered before the early 40s) , hell, even the formal definitions of a chaotic system and entropy are quite new. Should I start with learning basic probability theory if I havent done so by now? Will learning rigorous statistics help as well?