@article{AIHPB_2004__40_6_737_0,
author = {Carmona, Philippe and Petit, Fr\'ed\'erique and Yor, Marc},
title = {A trivariate law for certain processes related to perturbed brownian motions},
journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
pages = {737--758},
year = {2004},
publisher = {Elsevier},
volume = {40},
number = {6},
doi = {10.1016/j.anihpb.2003.11.004},
mrnumber = {2096216},
zbl = {1060.60082},
language = {en},
url = {https://www.numdam.org/articles/10.1016/j.anihpb.2003.11.004/}
}
TY - JOUR AU - Carmona, Philippe AU - Petit, Frédérique AU - Yor, Marc TI - A trivariate law for certain processes related to perturbed brownian motions JO - Annales de l'I.H.P. Probabilités et statistiques PY - 2004 SP - 737 EP - 758 VL - 40 IS - 6 PB - Elsevier UR - https://www.numdam.org/articles/10.1016/j.anihpb.2003.11.004/ DO - 10.1016/j.anihpb.2003.11.004 LA - en ID - AIHPB_2004__40_6_737_0 ER -
%0 Journal Article %A Carmona, Philippe %A Petit, Frédérique %A Yor, Marc %T A trivariate law for certain processes related to perturbed brownian motions %J Annales de l'I.H.P. Probabilités et statistiques %D 2004 %P 737-758 %V 40 %N 6 %I Elsevier %U https://www.numdam.org/articles/10.1016/j.anihpb.2003.11.004/ %R 10.1016/j.anihpb.2003.11.004 %G en %F AIHPB_2004__40_6_737_0
Carmona, Philippe; Petit, Frédérique; Yor, Marc. A trivariate law for certain processes related to perturbed brownian motions. Annales de l'I.H.P. Probabilités et statistiques, Tome 40 (2004) no. 6, pp. 737-758. doi: 10.1016/j.anihpb.2003.11.004
[1] , , , Some solvable stochastic control problems, Stochastics 4 (1) (1980) 39-83. | Zbl | MR
[2] , , Comportement asymptotique du nombre de tours effectués par la trajectoire brownienne plane, in: Sém. Probab. XXVIII, Lect. Notes Math, vol. 1583, Springer, Berlin, 1994, pp. 164-171. | Zbl | MR | Numdam
[3] , , Asymptotic windings of planar Brownian motion revisited via the Ornstein Uhlenbeck process, in: Sém. Probab. XXVIII, Lect. Notes Math, vol. 1583, Springer, Berlin, 1994, pp. 138-152. | Zbl | MR | Numdam
[4] , , Sur la loi des temps locaux browniens pris en un temps exponentiel, in: Sém. Probab. XXIII, Lect. Notes Math, vol. 1321, Springer, Berlin, 1988, pp. 454-466. | Zbl | MR | Numdam
[5] , , Valeurs principales associées aux temps locaux browniens, Bull. Sci. Maths. 2ème Sér 111 (1987) 23-101. | Zbl | MR
[6] , , Handbook of Brownian Motion: Facts and Formulae, Birkhaüser, 2002. | Zbl | MR
[7] , , , Some extensions of the arcsine law as (partial) consequences of the scaling property of Brownian motion, Probab. Theory Related Fields 100 (1994) 1-29. | Zbl | MR
[8] , , , An identity in law involving reflecting Brownian motion, derived from generalized arc-sine laws for perturbed Brownian motions, Stochastic Process. Appl 7 (1999) 323-333. | Zbl | MR
[9] , , , Beta variables as time spent in [0,∞[ by certain perturbed Brownian motions, J. London Math. Soc. (2) 58 (1999) 239-256. | Zbl
[10] , , , , On the laws of homogeneous functionals of the Brownian bridge, in: Studia Scientiarum Mathematicarum Hungarica, vol. 35, 1999, pp. 445-455. | Zbl | MR
[11] , , Pathwise uniqueness for perturbed versions of Brownian motion and reflected Brownian motion, Probab. Theory Related Fields 113 (nf 4) (1999) 519-534. | Zbl | MR
[12] , , Some Exercices in Probability, Cambridge University Press, 2003. | Zbl | MR
[13] , , Some properties of Brownian motion with a drift, and a generalization of a theorem of P. Lévy, Teor. Veroyatnost. i Primenen 44 (2) (1999) 466-472, English translation in , Theory Probab. Appl 44 (2) (2000) 412-418. | Zbl | MR
[14] , On some distributions concerning the maximum and minimum of a Wiener process, Proc. Colloq. Methods of Complex Anal. in the Theory of Probab. and Statist, Kossuth L. Univ. Debrecen, Debrecen, 1977, Colloq. Math. Soc. János Bolyai 21 (1979) 43-52. | Zbl | MR
[15] , , On two ergodic theorems for self-similar processes, in: Asymptotic Methods in Probability and Statistics, a volume in honour of Miklós Csörgő, 1998, pp. 97-111. | Zbl | MR
[16] , , , Some asymptotic properties of the local time of the uniform empirical process, Bernoulli 5 (6) (1999) 1035-1058. | Zbl | MR
[17] , , , Asymptotic behaviour of the local score of independent and identically distributed random sequences, Stochastic Process. Appl 107 (nf 1) (2003) 1-28. | Zbl | MR
[18] , Perturbed random walks and Brownian motions, and local times, New York J. Math 3A (June 9-13, 1997) 81-87, (electronic). | Zbl
[19] , , Perturbed and non-perturbed Brownian taboo processes, Ann. Inst. H. Poincaré 37 (2001) 725-736. | Zbl | MR | Numdam
[20] , , , Perturbed Bessel processes, in: Séminaire de Probabilités XXXII, Lecture Notes in Math, vol. 1686, Springer, Berlin, 1998, pp. 237-249. | Zbl | MR | Numdam
[21] , Un théorème de Ray-Knight lié au supremum des temps locaux, Probab. Theory Related Fields 87 (1990) 79-95. | Zbl
[22] , A converse to a theorem of P. Lévy, Ann. Probab 15 (1987) 1515-1523. | Zbl | MR
[23] , , , On weak Brownian motions of arbitrary order, Ann. Institut H. Poincaré 36 (4) (2000) 447-487. | Zbl | MR | Numdam
[24] , , , Pricing path-dependent options in some Black-Scholes market, from the distribution of homogeneous Brownian functionals, J. Appl. Probab 41 (1) (2004). | Zbl
[25] , , An extension of P. Lévy's distributional properties to the case of a Brownian motion with drift, Bernoulli 6 (4) (2000) 615-620. | Zbl | MR
[26] , , The limits of Sinaï's simple random walk in random environment, Ann. Probab 26 (4) (2000) 1477-1521. | Zbl | MR
[27] , Application du grossissement de filtration à l'étude des temps locaux du mouvement brownien, in: Lect. Notes Math, vol. 1118, Springer, Berlin, 1985. | Zbl
[28] , , Brownian Motion and Stochastic Calculus, Springer, Berlin, 1991. | Zbl | MR
[29] , A note on the structure of processes the measure of which is absolutely continuous with respect to the Wiener process modulus, Stochastics 8 (1982) 39-44. | Zbl | MR
[30] , , Excursions browniennes et carrés de processus de Bessel, C. R. Acad. Sci. Sér. I 303 (1986) 73-76. | Zbl | MR
[31] , , Enlacements du mouvement brownien autour des courbes de l'espace, Trans. Amer. Math. Soc. Sér. I 317 (1990) 687-722. | Zbl | MR
[32] , Special Functions and Their Applications, Dover Publications, New York, 1972, Translated and edited by Richard A. Silverman. | Zbl | MR
[33] , Intégrales stochastiques IV, in: Sém. Probab. I, Lect. Notes Math, vol. 39, Springer, Berlin, 1967, pp. 142-162. | Zbl | MR | Numdam
[34] , , Brownian analogues of Burke's theorem, Stochastic Process. Appl 96 (2) (2001) 285-304. | Zbl | MR
[35] , An excursion approach to Ray-Knight theorems for perturbed Brownian motion, Stochastic Process. Appl 63 (1) (1996) 67-74. | Zbl
[36] , , Perturbed Brownian motions, Probab. Theory Related Fields 108 (3) (1997) 357-383. | Zbl | MR
[37] F. Petit, Sur le temps passé par le mouvement brownien au-dessus d'un multiple de son supremum, et quelques extensions de la loi de l'arcsinus, PhD Thesis, Université Paris VII, 1992.
[38] , Quelques extensions de la loi de l'arcsinus, C. R. Acad. Sci. Sér. I 315 (1992) 855-858. | Zbl | MR
[39] F. Petit, Document de synthèse pour l'habilitation à diriger des recherches, Laboratoire de Probabilités et Modèles Aléatoires, Université Paris VI, décembre 2003.
[40] , , Itô's formula and the marginals of certain submartingales, Journées sur les Mathématiques financières (1998) 164-167.
[41] , The stochastic differential equations solved by local times of a Brownian excursion or bridge derived from the height profile of a random tree or forest, Ann. Probab 27 (1) (1999) 261-283. | Zbl | MR
[42] , , A decomposition of Bessel Bridges, Z. Wahr. Verw. Geb 59 (1982) 425-457. | Zbl | MR
[43] , , Quelques identités en loi pour les processus de Bessel, in: Astérisque. Hommage à P.A. Meyer et J. Neveu, vol. 236, Société Mathématique de France, 1996, pp. 249-276. | Zbl | MR | Numdam
[44] , , Path decompositions of a Brownian bridge related to the ratio of its maximum and amplitude, Studia Sci. Math. Hungar 35 (3-4) (1999) 457. | Zbl
[45] , , Laplace transforms related to excursions of a one-dimensional diffusion, Bernoulli 5 (2) (1999) 249-255. | Zbl | MR
[46] , Some remarks on Pitman's theorem, in: Sém. Probab. XXXI, Lect. Notes Math, vol. 1655, Springer, Berlin, 1997, pp. 266-271. | Zbl | MR | Numdam
[47] , , Continuous Martingales and Brownian Motion, Springer, Berlin, 1999. | Zbl | MR
[48] , On the martingales obtained by an extension due to Saisho, Tanemura and Yor, of Pitman's theorem, in: Sém. Probab. XXXI, Lect. Notes Math, vol. 1655, Springer, 1997, pp. 325-365. | Zbl | MR | Numdam
[49] , On square-root boundaries for Bessel processes, and pole-seeking Brownian motion, in: , (Eds.), Stochastic Analysis and Applications, Lect. Notes Math, vol. 1095, Springer, Berlin, 1984. | Zbl | MR
[50] , Some Aspects of Brownian Motion. Part I: Some Special Functionals, in: Lect. Math, Birkhaüser, ETH Zürich, 1992. | Zbl | MR
[51] , Random Brownian scaling and some absolute continuity relationships, in: Prog. Probab, vol. 36, Birkhaüser, 1995, pp. 243-252. | Zbl | MR
[52] , Some Aspects of Brownian Motion. Part II: Some Recent Martingale Problems, in: Lect. Math, Birkhaüser, ETH Zürich, 1997. | Zbl | MR
[53] , Some remarks about the joint law of Brownian motion and its supremum, in: Sém. Probab. XXXI, Lect. Notes Math, vol. 1655, Springer, Berlin, 1997, pp. 306-314. | Zbl | MR | Numdam
Cité par Sources :






