Hostname: page-component-78c5997874-t5tsf Total loading time: 0 Render date: 2024-11-09T12:38:44.776Z Has data issue: false hasContentIssue false
  • English
  • Français

Sur une caractérisation des vidanges fortes: corrections and extensions

Published online by Cambridge University Press:  14 July 2016

Jean-Guy Dion
Jean-Guy Dion*
Affiliation:
Université de Sherbrooke
Get access Rights & Permissions [Opens in a new window]

Abstract

A draining is a stochastic process defined by an urn scheme where the successive drawings are made without replacement and according to a drawing algorithm associated with a weighted graph. A draining is said to be a strong one if the number of balls which can be drawn from the urn (under the algorithm) converges in probability to the total number of balls in the urn at the beginning of the drawing when it goes to infinity. In particular, drainings associated with complete graphs having equal weights are found to be strong and for some others associated weighted graphs, strong drainings exist.

Keywords

DRAINING PROCESSRANDOM GRAPHNON-STATIONARY MARKOV PROCESSNON-STATIONARY URN DRAWINGVERTEX-SYMMETRIC GRAPH
Type
Research Papers
Information
Journal of Applied Probability , Volume 15 , Issue 2 , June 1978 , pp. 268 - 279
Copyright
Copyright © Applied Probability Trust 1978 

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

Berge, C. (1958) Théorie des graphes et ses applications. Dunod, Paris.Google Scholar
Bruneau, C. M. (1966) Théorie des graphes stochastiques appliquées à la synthèse et à la dégradation aléatoire des composés moléculaires multifonctionnels. Thèse de Doctorat ès Sciences Physiques. Ann. Chimie. Google Scholar
Diet, J. P. and Raynaud, H. (1977) Strong drainings associated to graphs with two vertices. J. Discrete Math. To appear.Google Scholar
Dion, J. G. (1976a) Sur une caractérisation des vidanges fortes, Adv. Appl. Prob. 8, 105–126.CrossRefGoogle Scholar
Dion, J. G. (1976b) De plus en plus fortes? … ou les avatars d'une conjecture sur les vidanges. Thèse de Doctorat 3e Cycle. Université Scientifique et Médicale de Grenoble. Unpublished.Google Scholar
Dion, J. G. and Raynaud, H. (1977a) Quelques nouvelles conditions suffisantes pour qu'une vidange soit forte. Actes du colloque international sur la théorie des graphes et les problèmes combinatoires. C.N.R.S., Orsay, France, 9–13 July 1976.Google Scholar
Dion, J. G. and Raynaud, H. (1977b) On new results for strong draining. Proceedings of the First International Conference on Mathematical Modelling. St. Louis, Missouri, 29 August-1 September 1977.Google Scholar
Kemeny, J. G. and Snell, J. L. (1960) Finite Markov Chains. Van Nostrand, Princeton, N.J.Google Scholar
Petry, F. (1971) Résolution d'une conjecture issue de la théorie des graphes aléatoires. Thèse de Doctorat 3e Cycle. Faculté des Sciences de Paris. Unpublished.Google Scholar
Raynaud, H. (1968) Sur les graphes aléatoires. Thèse de Doctorat ès Sciences Mathématiques. Ann. Inst. H. Poincaré 4, 255–329.Google Scholar
Raynaud, H. (1976) Strong drainings and sampling problems. In Recent Developments in Statistics, Proceedings of the European Meeting of Statisticians, Grenoble, 1976. North-Holland, Amsterdam.Google Scholar
Roberts, H. (1976) Discrete Mathematical Models. Prentice-Hall, Englewood Cliffs, N.J.Google Scholar