Hostname: page-component-586b7cd67f-rdxmf Total loading time: 0 Render date: 2024-11-26T18:05:47.812Z Has data issue: false hasContentIssue false
  • English
  • Français

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.
Get access Rights & Permissions [Opens in a new window]

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 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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