Markov Processes for Stochastic Modeling, 2nd Edition

9

Brownian Motion

9.1 Introduction

Brownian motion is a stochastic process that has applications in fields as vast and different as economics, biology, and management science. Mathematically, it can be thought of as a continuous-time process in which over every infinitely small time interval the entity under consideration moves one “step” in a certain direction. This suggests that Brownian motion can be viewed as a “random walk” process, which we will demonstrate shortly.

The physical manifestation of Brownian motion was observed by the Scottish botanist Robert Brown in 1827. His interpretation of this process was based on the movement of small ...