In this section, we will start by describing Brownian motion, and then procede in two directions: One of them will be to briefly introduce the topic of “Stochastic Differential Equations” through some of its historical landmarks and modern applications. The second will be the use of tools emanating from Brownian motion to study properties of plasmas.



Let’s start by defining Brownian Motion or Random Walks.


Imagine a drunk person walking on the street, not knowing where he is or where he wants to go! What will happen? He makes a step to the right. Then he might step to the left or to the right with equal probabilities! Obviously the average distance he will walk from his starting point is zero.