Journal of Integral Equations and Applications

Numerical solution of an integral equation from point process theory

R.S. Anderssen, A.J. Baddeley, F.R. de Hoog, and G.M. Nair

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We propose and analyze methods for the numerical solution of an integral equation which arises in statistical physics and spatial statistics. Instances of this equation include the Mean Field, Poisson-Boltzmann and Emden equations for the density of a molecular gas, and the Poisson saddlepoint approximation for the intensity of a spatial point process. Conditions are established under which the Picard iteration and the under relaxation iteration converge. Numerical validation is included.

Article information

J. Integral Equations Applications, Volume 26, Number 4 (2014), 437-452.

First available in Project Euclid: 9 January 2015

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60G55: Point processes
Secondary: 45B05: Fredholm integral equations 60H20: Stochastic integral equations 65R20: Integral equations

Intensity of point processes Lambert W function Fourier convolution Picard iteration Mean Field Poisson-Boltzmann and Emden equations


Anderssen, R.S.; Baddeley, A.J.; Hoog, F.R. de; Nair, G.M. Numerical solution of an integral equation from point process theory. J. Integral Equations Applications 26 (2014), no. 4, 437--452. doi:10.1216/JIE-2014-26-4-437.

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