Brownian motion is a stochastic process of great theoretical importance, and as the basic building block of a variety of other processes, of great practical importance as well. In this chapter we study Brownian motion and a number of random processes that can be constructed from Brownian motion. We also study the Ito stochastic integral and the resulting calculus, as well as two remarkable representation theorems involving stochastic integrals.

- Standard Brownian Motion
- Absolute Brownian Motion
- Brownian Motion with Drift and Scaling
- Reflected Brownian Motion
- Geometric Brownian Motion
- Brownian Bridge
- Integrated Brownian Motion
- Two-Dimensional Brownian Motion
- Hitting Time Experiment

- Stochastic Processes. Sheldon Ross
- Probability and Measure. Patrick Billingsley
- Probability: Theory and Examples. Richard Durrett
- Probability and Random Processes. Geoffrey Grimmett and David Stritzaker
- Investigations on the Theory of the Brownian Movement. Albert Einstein

The theory says a lot, but does not really bring us any closer to the secret of the

—Albert Einstein*old one*. I, at any rate, am convinced that He does not throw dice.