Vectorising a For-Loop Operation
 

<p>I have an SDE im approximating by a numerical scheme using the code:</p>

<pre><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
</code></pre>

<p>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.</p>

<p>Any help is appreciated</p>



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