Week 3 - Brown motion in 2-D

Below is the solution for the Brown motion in 2-D problem using simple Monte-Carlo simulation.


The mean x^2 and y^2 have a linear dependence from the number of steps (N) and the displacement R has a non-linear (y~f(x^0.5)) dependence. The mean values are calculated for a 1000 paths.Please notice that neither x^2 or y^2 can have a value larger than N^2. This should have been a good checking point for the validity of your simulation.