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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Abstract

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

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

Dates
First available in Project Euclid: 9 January 2015

Permanent link to this document
https://projecteuclid.org/euclid.jiea/1420812880

Digital Object Identifier
doi:10.1216/JIE-2014-26-4-437

Mathematical Reviews number (MathSciNet)
MR3299826

Zentralblatt MATH identifier
1346.60064

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

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

Citation

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. https://projecteuclid.org/euclid.jiea/1420812880


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