Vectorising a For-Loop Operation

[poster]

I have an SDE im approximating by a numerical scheme using the code:

mu = 1.5;

Sigma = 0.5;

TimeStep = 0.001;

Time = 0:TimeStep:5;

random1 = normrnd(2,0.05,[1,500]);

random2 = randn(1,length(Time));

X = zeros(500, length(Time));



for j = 1:500

   X(j,1)= random1(j);

   for i = 1:length(Time)

        X(j,i+1) = X(j,i) - mu*X(j,i)*TimeStep + Sigma*sqrt(2*mu)*sqrt(TimeStep)*random2(i);

   end

end

How would it be possible to remove the outer for-loop and vectorize so that at each time step, the first value is calculated for all 500 plots.

Any help is appreciated

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