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Statistique des processus de Poisson stationnaires de sous-varietes lineaires affines

Published online by Cambridge University Press:  01 July 2016

A. Fellous  and
J. Granara
A. Fellous*
Affiliation:
Université René Descartes
J. Granara*
Affiliation:
Université Pans VII
*
∗Postal address: UER de Mathématiques Logique Formelle et Informatique, Université René Descartes, 12 rue Cujas, 75005 Paris, France.
∗∗Postal address: UER de Mathématiques, Université Paris VII, 2 place Jussieu, 75006 Paris, France.
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Abstract

This paper reviews the principal properties of stationary Poisson processes of k-dimensional linear affine subvarieties in a d-dimensional vector space, and outlines basic results for the estimation of parameters from a single incomplete realization of the process.

Keywords

POISSON PROCESSGEOMETRICAL PROBABILITYSTATIONARITYSTATISTICS OF PROCESSES
Type
Research Article
Information
Advances in Applied Probability , Volume 13 , Issue 1 , March 1981 , pp. 84 - 92
Copyright
Copyright © Applied Probability Trust 1981 

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References

Bibliographie

[1] Bourbaki, N. (1956) Integration, 3ème edition. Hermann, Paris.Google Scholar
[2] Cox, D. R. and Lewis, P. A. W. (1969) L'analyse statistique des séries d'événements. Dunod, Paris.Google Scholar
[3] Davidson, R. (1974a) Stochastic processes of flats and exchangeability. Thesis, Part II. In Stochastic Geometry, ed. Harding, E. F. and Kendall, D. G., Wiley, New York.Google Scholar
[4] Davidson, R. (1974b) Construction of line processes: second-order properties. In Stochastic Geometry, ed. Harding, E. F. and Kendall, D. G., Wiley, New York.Google Scholar
[5] Fellous, A. (1976) Estimation dans les modèles de processus de Cox isotropes de droites et d'axes du plan. Thèse de 3ème cycle, Université Paris V.Google Scholar
[6] Granara, J. (1976) Compléments à la théorie des processus ponctuels et statistique des processus de Cox stationnaires d'hyperplans orientés. Thèse de 3ème cycle, Université Paris V.Google Scholar
[7] Kallenberg, O. (1976) On the structure of stationary flat processes. Z. Wahrscheinlichkeitstheorie. 37, 157–174.Google Scholar
[8] Kallenberg, O. (1977) A counterexample to R. Davidson's conjecture on line processes. Math. Proc. Camb. Phil. Soc. 82, 301–307.Google Scholar
[9] Kallenberg, O. (1980) On the structure of stationary flat processes. Z. Wahrscheinlichkeitsth. 52, 127–148.Google Scholar
[10] Krickeberg, K. (1974) Invariance properties of the correlation measure of line processes. In Stochastic Geometry, ed. Harding, E. F. and Kendall, D. G., Wiley, New York.Google Scholar
[11] Krickeberg, K. (1976–77) Processus ponctuels. Cours polycopié. UER de MLFI, Université Paris V.Google Scholar
[12] Krickeberg, K. (1976) Empirical Distribution and Processes. Lecture Notes in Mathematics 566, Springer-Verlag, Berlin.Google Scholar
[13] Papangelou, F. (1976) Point processes on spaces of flats and other homogeneous spaces. Math. Proc. Camb. Phil Soc. 80, 297–314.Google Scholar