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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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How to prove that the KL divergence is increasing with more noise

Assume I have a continuous random variable $X$, whose support is all $\mathbb R$. Let $Z$ be a standard normal independent on $X$, and let $$Y = X + \sigma Z$$ $Y$ essentially is equal to $X$ plus …
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