Introduction to Brownian Motion
Brownian motion (BM) as a continuous-time extension to a simple symmetric random walk has been introduced in this chapter. The stationary and independent increments, normal distribution, and Markovian property have been provided as the properties of a standard Brownian motion. Brownian motion with drift, and geometric Brownian motion have also been defined as an extension to a standard Brownian motion. Some examples and problems have been provided to clarify the basic and other properties of a Brownian motion.