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Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory.
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Is there an inequality relation between KL-divergence and $L_2$ norm?
Such inequality is impossible: consider $p(x)=1$, $q(x)=1/(2\sqrt{x})$, as probability densities on $(0,1)$. Then $D_{KL}(p\parallel q)$ is finite, while $\|p-q\|_2=\infty$, as $q\not\in L^2$.
The rev …