Abstract
A combinatorial (inclusion-exclusion) approach to the construction of point processes starting from densities is proposed. A formal sufficient crifficient criterion is derived and then applied with positive results to systems of functions having a special product form. Thus, a new class of point processes is derived to play a role within classical Gibbs processes.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Matthes K., Kerstan J., and Mecke J.: Infinitely Divisible Point Processes, Wiley, Chichester (1978).
Ambartzumian, R. V.: Factorization Calculus and Geometric Probability, Cambridge University Press, 1990.
Schuerer F.: Ueber die Funktional-Differentialgleichung f ′(x+1)=αf(x), Berichte Verhandlungen kgl. sachs. Ges. Wiss. zu Leipzig, Math.-phys. Kl. 64 (1912), 167–236.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Ambartzumian, R.V., Sukiasian, H.S. Inclusion-exclusion and point processes. Acta Appl Math 22, 15–31 (1991). https://doi.org/10.1007/BF00047649
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00047649