Approximating integrals of multivariate exponentials: A moment approach

Authors:
Dimitris Bertsimas;Xuan Vinh Doan;Jean Lasserre
Affiliations:
Sloan School of Management, Operations Research Center, Massachusetts Institute of Technology, E40-147, Cambridge, MA 02139-4307, USA;Operations Research Center, Massachusetts Institute of Technology, Cambridge, MA 02139-4307, USA;LAAS, 7 Avenue Du Colonel Roche, 31077 Toulouse Cédex 4, France
Venue:
Operations Research Letters
Year:
2008

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Abstract

We propose a method to calculate lower and upper bounds of some exponential multivariate integrals using moment relaxations and show that they asymptotically converge to the value of the integrals when the moment degree increases. We report computational results for integrals involving the normal distribution and exponential order statistic probabilities.