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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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derivative of conditional expectation

Suppose $H:\Omega\times X\mapsto Y$ for some borel subset $X\subset \mathbf{R}$, Euclidean space $Y$, and probability space $(\Omega, \mathcal{F},P)$. Further suppose that $H$ is $C^1$ for each fixed …