1. Random. 2. Following a random distribution pattern, such that its probability may be analyzed statistically, but not predicted precisely. 3. (Rare) Pertaining to conjecture, speculation.

What I think is missing from all three of these is the element of a stochastic process having a present moment and a built-in mechanism of some kind -- although the concession in definition 2 that such a process "may be analysed statistically" does get a good deal of the way there. (I see that I've used the ambiguous word "moment" above, and my subconscious must be at work here: I think that stochastic has an element of moment, i.e. of inertia or past history, as opposed to total randomness, to it.