## Quadratic Variation and Stochastic Integration

*Stochastic integration was first developed in the context of the Brownian motion and the theory was then extended to martingales with continuous paths, which we will call continuous martingales in what follows. Continuous martingales have a lot of structure which eases the corresponding stochastic integration theory. The quadratic variation of a continuous martingale is the central concept in this theory. The purpose of this note is to provide an easy introduction to this subject before presenting Ito calculus in a later post.*