I was reading an article and I saw the following sentence:
For a given martingale, if it has an upper or a lower bound, then the
martingale must converge (a.s.). Since the likelihood is always
nonnegative, 0 is a lower bound.
What does “a.s.” stand for? Is it a common usage?
My guess is “asymptotically” but I’d like to verify.
It stands for “almost surely,” i.e. the probability of this occurring is 1.