__RANDOM WALKS__

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.