How to generate iid Gaussian noise vector
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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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Ben McMahon
el 14 de Jul. de 2021
Editada: Ben McMahon
el 15 de Oct. de 2021
For your particular example as your covariance is idenity and your mean 0, this is a mulitvariate standard normal distrbuiton:
~
% 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
el 19 de Jul. de 2021
A Gaussian distribution and a normal distribution are two names for the same thing. See the Wikipedia entry for normal distribution.
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