Derivatives of probability functions and integrals over sets given by inequalities
type: Item
instance of: scholarly article
title: Derivatives of probability functions and integrals over sets given by inequalities
zbMATH Open document ID: 0826.60054
DOI: 10.1016/0377-0427(94)90388-3
published in: Journal of Computational and Applied Mathematics
publication date: 1995-08-07T00:00:00Z
review text: The problem is to find the gradient of probability functions \(F = F(x)\) being represented as integrals over sets \(B = B(x)\) given by a finite number of inequalities, \(f_i (x,y) \leq 0\), \(i = 1, \ldots, m\), where the integrand \(p = p(x,y)\) (probability density) as well as the constraints \(f(x,y) \leq 0\) depend on a certain parameter vector \(x\). The gradient with respect to \(x\) is represented here as the sum of integrals taken over a volume and over a surface. The results are applied to the calculation of the gradient of probability functions arising in chance- constrained programming.
reviewed by: Kurt Marti
Mathematics Subject Classification ID: 60H99
zbMATH DE Number: 773896
zbMATH Keywords: gradient of probability functions
zbMATH Keywords: chance-constrained programming
author: Stanislav P. Uryasev
MaRDI profile type: Publication
full work available at URL: 0377-0427(94)90388-3
OpenAlex ID: W2093304942
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description: scientific article; zbMATH DE number 773896