Brownian Motion Calculus - Review
This book gives a non-rigorous treatment to Brownian motion and its applications to finance. Let me summarize a few points from various chapters.
Chapter 1 : Brownian motion
This chapter starts off by specifying Brownian motion by the properties of its increments such as independence, first and second moments, transition density etc. A discrete approximation of BM is shown via a binomial tree. Covariance of BM process is derived. A way to manufacture correlated BM is shown.