%Simulation of the Brownian Motion

%Clear all variables and screen
clear all; clc;

%Parameters
h = 0.1;         %Time step
n = 10;          %Number of time steps
T = n*h;         %Maturity date
time = 0:h:T;    %Vector of dates
n_traj = 100000  %Number of trajectories

%Simulation of one path of a one-dimensional Brownian motion
tic
W = zeros(n_traj,n+1);
Z = normrnd(0,sqrt(h),n_traj,n);
%NOTE Beaucoup plus rapide de faire un seul appel ŕ la fonction normrnd que
%de generer des v.a. normales ŕ l'intérieur de la boucle.
for i = 1:n
    W(:,i+1) = W(:,i) + Z(:,i);
end
toc

(mean(W))';
(std(W).*std(W))';