3. Brownian motion

3.1 Construction of Brownian motion

Brownian motion, or the Wiener process, plays a fundamental role in many fields. It was introduced by Bachelier in 1900, for applications in finance, and is again playing an important role in financial mathematics today. It was rediscovered shortly after Bachelier by Einstein, and has since become one of the major modeling tools in physics. It can be found at $W={\left(W_t\right)}_{t\ge 0}$ .

It can be constructed in a number of different ways. The most common definitions of Brownian motion...