How to generate iid Gaussian noise vector

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Muhammad Yasir
Muhammad Yasir 2021-7-14
编辑： Ben McMahon 2021-10-15
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...

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回答（1 个）

Ben McMahon
Ben McMahon 2021-7-14
编辑：Ben McMahon 2021-10-15
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.
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Ben McMahon
Ben McMahon 2021-7-19
A Gaussian distribution and a normal distribution are two names for the same thing. See the Wikipedia entry for normal distribution.
Muhammad Yasir
Muhammad Yasir 2021-8-12
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

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