How to study stochastic calculus

And why you are probably doing it wrong.

A sample simulation of a stochastic process. Image credit: https://people.duke.edu/~rnau/411rand.htm

Stochastic calculus, as its name suggests: is an area of mathematics concerned with the calculus (e.g. derivatives, integrals, limits, etc.) of stochastic processes (also known as random processes, effectively sequences of random numbers which possess certain properties). It is a natural extension of ordinary calculus to functions of a random variable, which are not…