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Derivatives of probability functions and some applications

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Probability functions depending upon parameters are represented as integrals over sets given by inequalities. New derivative formulas for the intergrals over a volume are considered. Derivatives are presented as sums of integrals over a volume and over a surface. Two examples are discussed: probability functions with linear constraints (random right-hand sides), and a dynamical shut-down problem with sensors.

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Uryasev, S. Derivatives of probability functions and some applications. Ann Oper Res 56, 287–311 (1995).

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