Stochastic Calculus Theory and Formalisms

This is a brief tutorial on how to do informal stochastic calculus and why it works. I state all the theoretical results needed to compute, I properly compute solutions to two famous SDEs, and I show you how to get the same answers by manipulating Leibniz notation. Then I shows how the Leibniz notation relates to all those theoretical results (there is a neat sort of “lexical isomorphism”). Finally, I show how the Leibniz notation is really helpful–more helpful than the theory–when it comes to solving problems. In particular, it can help you figure out what function to plug in to Ito’s formula.