Applications de la théorie spectrale des cordes vibrantes aux fonctionnelles additives principales d'un brownien réfléchi

Jean Bertoin

Annales de l'I.H.P. Probabilités et statistiques (1989)

  • Volume: 25, Issue: 3, page 307-323
  • ISSN: 0246-0203

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Bertoin, Jean. "Applications de la théorie spectrale des cordes vibrantes aux fonctionnelles additives principales d'un brownien réfléchi." Annales de l'I.H.P. Probabilités et statistiques 25.3 (1989): 307-323. <http://eudml.org/doc/77354>.

@article{Bertoin1989,
author = {Bertoin, Jean},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {additive functionals; reflected Brownian motion; local time; vibrating strings},
language = {fre},
number = {3},
pages = {307-323},
publisher = {Gauthier-Villars},
title = {Applications de la théorie spectrale des cordes vibrantes aux fonctionnelles additives principales d'un brownien réfléchi},
url = {http://eudml.org/doc/77354},
volume = {25},
year = {1989},
}

TY - JOUR
AU - Bertoin, Jean
TI - Applications de la théorie spectrale des cordes vibrantes aux fonctionnelles additives principales d'un brownien réfléchi
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 1989
PB - Gauthier-Villars
VL - 25
IS - 3
SP - 307
EP - 323
LA - fre
KW - additive functionals; reflected Brownian motion; local time; vibrating strings
UR - http://eudml.org/doc/77354
ER -

References

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  2. [2] Ph. Biane et M. Yor, Valeurs principales associées aux temps locaux Browniens, Bull. Sc. Math.2e série, t. 111, 1987, p. 23-101. Zbl0619.60072MR886959
  3. [3] N.H. Bingham, Fluctuation theory in continuous time, Adv. Appl. Probab., vol. 7, 1975, p. 705-766. Zbl0322.60068MR386027
  4. [4] J. Bretagnolle, p-variation de fonctions aléatoires. 2e partie : Processus à accroissements indépendants, in Séminaire de Probabilités VI; Lect. Notes in Math., n° 258; Springer-Verlag, 1972, p. 64-71. Zbl0273.60052MR373020
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  9. [9] I.S. Kac, Integral Characteristics of the Growth of Spectral Functions for Generalized Second Order Boundary Problems with Conditions at Regular End, Math. U.S.S.R. Izv., vol. 5, 1971, p. 161-191. Zbl0285.34017
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  11. [11] S. Kotani et S. Watanabe, Krein's Spectral Theory of Strings and General Diffusion Processes, in M. FUKUSHIMA éd, Functional Analysis in Markov Processes, Proceeding Zbl0496.60080
  12. Katata and Kyoto1981, Lect. Notes in Math., n° 923 : Springer Verlag, 1981, p. 235- 259. 
  13. [12] M.G. Krein, Sur la généralisation d'une recherche de Stieltjes, Dok. Akad. Nauk. S.S.S.R., vol. 87, 1952, p. 881-884. Zbl0049.34702
  14. [13] M.G. Krein, Sur quelques cas de détermination effective des densités d'une corde inhomogène à partir de sa fonction spectrale, Dokl. Akad. Nauk. S.S.S.R., vol. 93, 1953, p. 617-620. Zbl0053.24605
  15. [14] T. Yamada, On the Fractional Derivative of Brownian Local Times, J. Math. Kyoto Univ., vol. 25-1, 1985, p. 49-58. Zbl0625.60090MR777245
  16. [15] T. Yamada, On Some Limit Theorems for Occupation Times of One Dimensional Brownian Motion and its Continuous Additive Functionals Locally of Zero Energy, J. Math. Kyoto Univ., vol. 26-2, 1986, p. 309-322. Zbl0618.60080MR849222

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