Someone once asked my what my favourite theorem was. This seemed an odd question. I sort of blustered and said “bluh, uh, optional stopping?”, although later wondered if I should have gone for max-flow min-cut.
Sometime later, I decided to make a blog. “Optional Stopping” seemed to be a terribly good title for two reasons: 1) because it is Officially My Favourite Theorem, and 2) because it’s hi-lar-ious pun on the fact that I only write blog posts when I’m bored with doing proper work. Optional stopping. I choose to stop work. Geddit? Oh, never mind.
So, in case you don’t know, It thought this would be a good opportunity to explain what the optional stopping theorem is.
In this article, we look at stopping times, martingales and the OST itself, before giving a couple of (I think) nifty applications to random walks.
