What are and how to define indepedent unit wiener processes?

I currently read some papers where i find the term "mutually indepedent unit Wiener processes", is this term a form of Wiener definition and if so, how can i implement it in matlab? Does it mean that my result must have mean = 0, variance = 1? A paper example is http://pdfs.semanticscholar.org/d771/c6a665b40f6e0a8465a0e73f4810fffdacef.pdf (see section 2.1 ,2.2). I found some code for Wiener at https://me.ucsb.edu/~moehlis/APC591/tutorials/tutorial7/node2.html and implemented the following script

T = 1; N = 500;
dt = T/N;
dW = zeros(1,N); % preallocate arrays ...
W = zeros(1,N); % for efficiency
dW(1) = sqrt(dt)*randn; % first approximation outside the loop ...
W(1) = dW(1); % since W(0) = 0 is not allowed
for j = 2:N
dW(j) = sqrt(dt)*randn; % general increment
W(j) = W(j-1) + dW(j);
end
% figure;
% plot([0:dt:T],[0,W],'r-') % plot W against t
% xlabel('t','FontSize',16)
% ylabel('W(t)','FontSize',16,'Rotation',0)

% mean and variance

Mean1 = mean(W)
variance1 = var(W)

The mean is close to zero, but the variance is not close to one.