What Brownian Motion is?

An Easy App to Explain a Hard Concept

Ian Castillo Rosales
CIMAT

What the problem is?

In Mathematics we always have difficult concepts, but what if you can see them... Even control them!

With this app you can learn a concept a little bit difficul for many people. Do you know what Brownian Motion really is?

Definition. We said that \(B = (B_t, t \geq 0)\) is a real Brownian Motion that starts in \(0\) if \(B\) is a center Gaussian process such that \[ E\left[ B_s B_t \right] = COV. \]

Hard isn't?

What the Hell Brownian Motion is?

With this application you can play with Brownian Motion and understand the main facts about this randomness process in the nature.

What about history, any mathematical concept should be explained with some history of the concept, some book references and some advice to learned for yourself.

You even can see the code behind the app and reproduce the application in your computer, modife it and create something new!

Your options!

You have many option to get fun with Brownian Motion...

  • You can reproduce a LOT, really, a lot of Brownian Motion examples.
  • You can see the Brownian Motion through time or space.
  • You can see the evolution of Brownian Motion.
  • You can see a briefly summary of the movement of Brownian Motion.

A Small Test

So? Can you remember what Brownian Motion is?

  1. A Random process with the next characteristic: The correlation matrix between two times in the process should be equal to the maximum of the times.
  2. A Random process with the next characteristic: The covariance matrix between two times in the process should be equal to the minimum of the times.
  3. Really man? I even can't remember what I ate in the breakfast.
  4. I should use the Brownian Motion App.

Should be a random process.