(C) D. S. Grebenkov, Dataset created for the project INADILIC

A Brownian motion trajectory is generated as a cumulative
sum of independent Gaussian variables with mean 0 and 
variance 2D, with the diffusion coefficient D set to 1.

The full set contains M = 1000 one-dimensional trajectories 
of N = 10000 points (steps). 

The trajectories were generated in Matlab by the function 'BM.m'

The file 'BM_sample.txt' contains a column of positions.
The file 'BM_full.mat' can be opened in Matlab by commands:

A = load('BM_full.mat');   % structure containing the trajectories
X = A.X;                   % matrix of size MxN, X(m,:) is the m-th trajectory
clear A;
               
One can check that the mean square displacement satisfies 
the Einstein relation <X^2(t)> = 2Dt

plot(mean(X.^2));