It is known that the optional stopping theorem from martingale theory is a very powerful theorem in probability theory in statistics.
I have heard of a probability course at Stanford where martingales and optional stopping is introduced at the beginning, then much of the course material is derived from this principle.
Unfortunately there are no course notes. Does anyone know where I can find these kind of derivations, or for instance, whether it is possible to derive concentration bounds like Azuma's inequality from OST?