ABSTRACT
Brownian motion is probably the most important stochastic process in probability theory and applications. Some of its basic properties are developed in the rst half of this chapter, together with a brief discussion of martingales. Based on Brownian motion, the stochastic integrals and stochastic dierential equations are introduced, including an application in option pricing in a single stock market. This topic is more advanced than the rest of these notes. An eort is made to present a complete description without being bogged down in advanced theory. For a more complete treatment, the reader is referred to a standard text on stochastic dierential equations such as [7].
