= Hurstiness of independent sums
{c}
{title2=$H(X_n+Y_n)=\max(H(X_n),H(Y_n))$}
For independent real sequences, put the faster sequence at the slower speed by <slower-speed degeneration of a large deviation principle>, then use the <product large-deviation principle> and <contraction principle for large deviations> for addition. Unequal speeds give a translate of the slower sequence's rate. Equal speeds give the <infimal convolution> of the two rates. Its unique zero is the sum of their zero points, and a translated positive finite point has positive finite cost, since <compactness> attains each finite fiber <infimum>. Thus the defining nondegeneracy is preserved.
// Target: queueing-theory.bigb
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