How to generate iid Gaussian noise vector

I am trying to simulate algorithams given in a research paper.

How can I generate a noise sequence w_t, which is i.i.d. Gaussian of mean zero with variance 2I3 (2xI3 ,where I3 is identity matrix of dimension 3x3) and the initial condition is x_init = [10 10 −10]'

Kindly look at this segment of the paper for which I need to create Gaussian noise samples. I think gaussian noise is a column vector...

Answer 1

[Ben McMahon]

For your particular example as your covariance is idenity and your mean 0, this is a mulitvariate standard normal distrbuiton:

~

The simple answer to this is to use the randn function to generate your samples. For example

% Set Number of Samples
NumSamples = 1000;

% Prealloacte
w = zeros(3,NumSamples);

% Loop for each sample
for t = 1:NumSamples
    w(3,t) = randn(3,1); % Generate a 3x1 Random vector
end

Note that the inital condition is for the state vector of the SDE, x, and is not related to generating the white noise vectors.

[Muhammad Yasir]

Thank you for such an elaboration...

But what about Gaussian noise?

[Ben McMahon]

A Gaussian distribution and a normal distribution are two names for the same thing. See the Wikipedia entry for normal distribution.

[Muhammad Yasir]

i think it should be the code

mu = 0;

sigma = 10*eye(3)

R = chol(sigma);

w_t = repmat(mu,3,1) + randn(3,3)*R

for i=1:length(w_t(1,:))

for j=1:length(w_t(:,1))

phi(i,j) = ( 1 - exp( w_t(i,j) ) )/ ( 1 + exp( w_t(i,j) ) )

end

end