What Happened to Discrete Chaos, the Quenouille Process, and the Sharp Markov Property? Some History of Stochastic Point Processes
Peter Guttorp,
Thordis L. Thorarinsdottir,
Peter Guttorp
Department of Statistics, University of Washington, Box 354322, Seattle, WA 98195, USA
Norwegian Computing Center, P.O. Box 114 Blindern, NO-0314 Oslo, Norway
E-mail: [email protected]
Thordis L. Thorarinsdottir
Institute of Applied Mathematics, Heidelberg University, Im Neuenheimer Feld 294, D-69120 Heidelberg, Germany
E-mail: [email protected]
Peter Guttorp,
Thordis L. Thorarinsdottir,
Peter Guttorp
Department of Statistics, University of Washington, Box 354322, Seattle, WA 98195, USA
Norwegian Computing Center, P.O. Box 114 Blindern, NO-0314 Oslo, Norway
E-mail: [email protected]
Thordis L. Thorarinsdottir
Institute of Applied Mathematics, Heidelberg University, Im Neuenheimer Feld 294, D-69120 Heidelberg, Germany
E-mail: [email protected]
Summary
enThe use of properties of a Poisson process to study the randomness of stars is traced back to a 1767 paper. The process was used and rediscovered many times, and we mention some of the early scientific areas. The name Poisson process was first used in print in 1940, and we believe the term was coined in the corridors of Stockholm University some time between 1936 and 1939. We follow the early developments of doubly stochastic processes and cluster processes, and describe different efforts to apply the Markov property to point processes.
Résumé
esLe recours aux processus de Poisson dans l'étude de la distribution des étoiles remonte à une publication de 1767. Ce type de processus a été redécouvert et utiliséà maintes reprises, et nous mentionnons quelques-uns des domaines scientifiques où il l'a été pour la première fois. La première trace imprimée du nom “processus de Poisson” apparaît en 1940, et nous pensons que cette terminologie est née dans les couloirs de l'Université de Stockholm entre 1936 et 1939. Nous retraçons les premiers développements des processus doublement stochastiques et des processus de Poisson en grappes, et décrivons les efforts accomplis en vue d'appliquer aux processus ponctuels la propriété de Markov.
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