Open Access
WINTER 2014 Numerical solution of an integral equation from point process theory
R.S. Anderssen, A.J. Baddeley, F.R. de Hoog, G.M. Nair
J. Integral Equations Applications 26(4): 437-452 (WINTER 2014). DOI: 10.1216/JIE-2014-26-4-437


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.


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R.S. Anderssen. A.J. Baddeley. F.R. de Hoog. G.M. Nair. "Numerical solution of an integral equation from point process theory." J. Integral Equations Applications 26 (4) 437 - 452, WINTER 2014.


Published: WINTER 2014
First available in Project Euclid: 9 January 2015

zbMATH: 1346.60064
MathSciNet: MR3299826
Digital Object Identifier: 10.1216/JIE-2014-26-4-437

Primary: 60G55
Secondary: 45B05 , 60H20 , 65R20

Keywords: Fourier convolution , Intensity of point processes , Lambert W function , Mean field , Picard iteration , Poisson-Boltzmann and Emden equations

Rights: Copyright © 2014 Rocky Mountain Mathematics Consortium

Vol.26 • No. 4 • WINTER 2014
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