On the joint distribution of the maximum and its location for a linear diffusion

Endre Csáki; Antónia Földes; Paavo Salminen

Annales de l'I.H.P. Probabilités et statistiques (1987)

  • Volume: 23, Issue: 2, page 179-194
  • ISSN: 0246-0203

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Csáki, Endre, Földes, Antónia, and Salminen, Paavo. "On the joint distribution of the maximum and its location for a linear diffusion." Annales de l'I.H.P. Probabilités et statistiques 23.2 (1987): 179-194. <http://eudml.org/doc/77296>.

@article{Csáki1987,
author = {Csáki, Endre, Földes, Antónia, Salminen, Paavo},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {hitting-time densities; diffusion representation of Brownian local time; exponential time},
language = {eng},
number = {2},
pages = {179-194},
publisher = {Gauthier-Villars},
title = {On the joint distribution of the maximum and its location for a linear diffusion},
url = {http://eudml.org/doc/77296},
volume = {23},
year = {1987},
}

TY - JOUR
AU - Csáki, Endre
AU - Földes, Antónia
AU - Salminen, Paavo
TI - On the joint distribution of the maximum and its location for a linear diffusion
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 1987
PB - Gauthier-Villars
VL - 23
IS - 2
SP - 179
EP - 194
LA - eng
KW - hitting-time densities; diffusion representation of Brownian local time; exponential time
UR - http://eudml.org/doc/77296
ER -

References

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  1. [1] M. Abramowitz, I.A. Stegun, Handbook of Mathematical Functions. Dover, New York, 1965. 
  2. [2] A.N. Borodin, Distribution of integral functionals of Brownian motion (in Russian). Zap. Naucn. Sem. LOMI, t. 119, 1982, p. 19-38. Zbl0491.60082MR666084
  3. [3] K.L. Chung, Excursions in Brownian motion. Ark. Mat., t. 14, 1976, p. 155-177. Zbl0356.60033MR467948
  4. [4] A. Erdélyi (ed.). Tables of Integral Transforms, vol. I. McGraw-Hill, New York, Toronto, London, 1954. Zbl0055.36401MR61695
  5. [5] R.K. Getoor, Excursions of a Markov process. Ann. Prob., t. 7 (2), 1979, p. 244-266. Zbl0399.60069MR525052
  6. [6] J.-P. Imhof, Density factorizations for Brownian motion, meander and the three-dimensional Bessel process, and applications. J. Appl. Prob., t. 21, 1984, p. 500- 510. Zbl0547.60081MR752015
  7. [7] J.-P. Imhof, On Brownian bridge and excursion. Studia Sci. Math. Hungar (to appear). Zbl0625.60096MR885996
  8. [8] K. Itô, H. Mckean, Diffusion Processes and Their Sample Paths. Springer, Berlin, 1965. Zbl0127.09503MR345224
  9. [9] F.B. Knight, On the excursion process of Brownian motion. Trans. Amer. Math. Soc., t. 258, 1980, p. 77-86. Zbl0426.60073MR554319
  10. [10] P. Lévy, Processus Stochastiques et Mouvement Brownien. Gauthier-Villars, Paris, 1948. Zbl0034.22603MR190953
  11. [11] G. Louchard, Mouvement Brownien et valeurs propres du Laplacien. Ann. Inst. H. Poincaré, IV (4), 1968, p. 331-342. Zbl0181.20803MR261695
  12. [12] G. Louchard, Kac's formula, Lévy's local time and Brownian excursion. J. Appl. Prob., t. 21, 1984, p. 479-499, Zbl0551.60086MR752014
  13. [13] P. Mcgill, Markov properties of diffusion local time: a martingale approach. Adv. Appl. Prob., t. 14, 1982, p. 789-810. Zbl0502.60062MR677557
  14. [14] D. Ray, Sojourn times of diffusion processes. Illinois J. Math., t. 7, 1963, p. 615- 630. Zbl0118.13403MR156383
  15. [15] P. Salminen, Brownian excursions, revisited. Sem. Stochastic Processes, 1983, eds E. Çinlar, K. L. Chung, R. K. Getoor, Birkhäuser, Boston, 1984. Zbl0557.60067MR902418
  16. [16] L.A. Shepp, The joint density of the maximum and its location for a Wiener process with drift. J. Appl. Prob., t. 16, 1979, p. 423-427. Zbl0403.60072MR531776
  17. [17] L.J. Slater, Confluent Hypergeometric Functions. University Press, Cambridge, 1960. Zbl0086.27502MR107026
  18. [18] I. Vincze, Einige zweidimensionale Verteilungs- und Grenzverteilungssätze in der Theorie der geordneten Stichproben. Publ. Math. Inst. Hungar. Acad. Sci., t. 11, 1957, p. 183-203. Zbl0086.34005MR105172
  19. [19] D. Williams, Path decomposition and continuity of local time for one-dimensional diffusions. Proc. London Math. Soc., t. 28 (3), 1974, p. 738-768. Zbl0326.60093MR350881

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