Nicole Statler

Western Washington University
, BH 217

Abstract

Brownian Motion: Existence and Properties

The jittery motion of particles suspended in fluid or the movement of dust
due to air currents both have an aspect of randomness. This random nature
can be modeled by what is a key stochastic process known as Brownian motion.
In this talk we will build intuition about Brownian motion then discuss the
construction of this fundamental stochastic process. After the existence has
been proven, the history and some properties will be discussed. These properties
will give insight into the erratic nature of Brownian motion, but show it still has
very nice or regular behavior such as continuity. Finally, common applications
and specific interesting uses of Brownian motion will be explored.