Matilda Galmar: Martingales and Optional Stopping

Abstract: Consider a sequence of random variables. What can we say about their expected value? Can we say something about an arbitrary element in the sequence? What if we don't choose the element arbitrarily, but let another random variable make the choice?

To answer these questions (and even understand what they are even about) we will review some basic probability theory through a measure theoretic lens (even though measure theory is not needed to be able to follow this talk), and then move on to define what a martingale is and finish with the three optional stopping theorems and some examples.