no. 6
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. 
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     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},
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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. http://archive.numdam.org/articles/10.1016/j.anihpb.2003.11.004/

[1] V.E. Benes, L.A. Shepp, H.S. Witsenhausen, Some solvable stochastic control problems, Stochastics 4 (1) (1980) 39-83. | MR | Zbl

[2] J. Bertoin, W. Werner, 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. | Numdam | MR | Zbl

[3] J. Bertoin, W. Werner, 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. | Numdam | MR | Zbl

[4] Ph. Biane, M. Yor, 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. | Numdam | MR | Zbl

[5] Ph. Biane, M. Yor, Valeurs principales associées aux temps locaux browniens, Bull. Sci. Maths. 2ème Sér 111 (1987) 23-101. | MR | Zbl

[6] A. Borodin, P. Salminen, Handbook of Brownian Motion: Facts and Formulae, Birkhaüser, 2002. | MR | Zbl

[7] Ph. Carmona, F. Petit, M. Yor, Some extensions of the arcsine law as (partial) consequences of the scaling property of Brownian motion, Probab. Theory Related Fields 100 (1994) 1-29. | MR | Zbl

[8] Ph. Carmona, F. Petit, M. Yor, 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. | MR | Zbl

[9] Ph. Carmona, F. Petit, M. Yor, Beta variables as time spent in [0,∞[ by certain perturbed Brownian motions, J. London Math. Soc. (2) 58 (1999) 239-256. | Zbl

[10] Ph. Carmona, F. Petit, J. Pitman, M. Yor, On the laws of homogeneous functionals of the Brownian bridge, in: Studia Scientiarum Mathematicarum Hungarica, vol. 35, 1999, pp. 445-455. | MR | Zbl

[11] L. Chaumont, R.A. Doney, Pathwise uniqueness for perturbed versions of Brownian motion and reflected Brownian motion, Probab. Theory Related Fields 113 (nf 4) (1999) 519-534. | MR | Zbl

[12] L. Chaumont, M. Yor, Some Exercices in Probability, Cambridge University Press, 2003. | MR | Zbl

[13] A.S. Cherny, A.N. Shiryaev, 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. | MR | Zbl

[14] E. Csaki, 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. | MR | Zbl

[15] E. Csaki, A. Földes, 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. | MR | Zbl

[16] M. Csörgő, Z. Shi, M. Yor, Some asymptotic properties of the local time of the uniform empirical process, Bernoulli 5 (6) (1999) 1035-1058. | MR | Zbl

[17] J.J. Daudin, M.P. Etienne, P. Vallois, Asymptotic behaviour of the local score of independent and identically distributed random sequences, Stochastic Process. Appl 107 (nf 1) (2003) 1-28. | MR | Zbl

[18] B. Davis, Perturbed random walks and Brownian motions, and local times, New York J. Math 3A (June 9-13, 1997) 81-87, (electronic). | Zbl

[19] R.A. Doney, Y.B. Nakhi, Perturbed and non-perturbed Brownian taboo processes, Ann. Inst. H. Poincaré 37 (2001) 725-736. | Numdam | MR | Zbl

[20] R.A. Doney, J. Warren, M. Yor, Perturbed Bessel processes, in: Séminaire de Probabilités XXXII, Lecture Notes in Math, vol. 1686, Springer, Berlin, 1998, pp. 237-249. | Numdam | MR | Zbl

[21] N. Eisenbaum, Un théorème de Ray-Knight lié au supremum des temps locaux, Probab. Theory Related Fields 87 (1990) 79-95. | Zbl

[22] P. Fitzsimmons, A converse to a theorem of P. Lévy, Ann. Probab 15 (1987) 1515-1523. | MR | Zbl

[23] H. Föllmer, C.T. Wu, M. Yor, On weak Brownian motions of arbitrary order, Ann. Institut H. Poincaré 36 (4) (2000) 447-487. | Numdam | MR | Zbl

[24] T. Fujita, F. Petit, M. Yor, Pricing path-dependent options in some Black-Scholes market, from the distribution of homogeneous Brownian functionals, J. Appl. Probab 41 (1) (2004). | Zbl

[25] S.E. Graversen, A.N. Shiryaev, An extension of P. Lévy's distributional properties to the case of a Brownian motion with drift, Bernoulli 6 (4) (2000) 615-620. | MR | Zbl

[26] Y. Hu, Z. Shi, The limits of Sinaï's simple random walk in random environment, Ann. Probab 26 (4) (2000) 1477-1521. | MR | Zbl

[27] T. Jeulin, 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] I. Karatzas, S. Shreve, Brownian Motion and Stochastic Calculus, Springer, Berlin, 1991. | MR | Zbl

[29] G.N. Kinkladze, 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. | MR | Zbl

[30] J.F. Le Gall, M. Yor, Excursions browniennes et carrés de processus de Bessel, C. R. Acad. Sci. Sér. I 303 (1986) 73-76. | MR | Zbl

[31] J.F. Le Gall, M. Yor, Enlacements du mouvement brownien autour des courbes de l'espace, Trans. Amer. Math. Soc. Sér. I 317 (1990) 687-722. | MR | Zbl

[32] N.N. Lebedev, Special Functions and Their Applications, Dover Publications, New York, 1972, Translated and edited by Richard A. Silverman. | MR | Zbl

[33] P.A. Meyer, Intégrales stochastiques IV, in: Sém. Probab. I, Lect. Notes Math, vol. 39, Springer, Berlin, 1967, pp. 142-162. | Numdam | MR | Zbl

[34] N. O'Connell, M. Yor, Brownian analogues of Burke's theorem, Stochastic Process. Appl 96 (2) (2001) 285-304. | MR | Zbl

[35] M. Perman, An excursion approach to Ray-Knight theorems for perturbed Brownian motion, Stochastic Process. Appl 63 (1) (1996) 67-74. | Zbl

[36] M. Perman, W. Werner, Perturbed Brownian motions, Probab. Theory Related Fields 108 (3) (1997) 357-383. | MR | Zbl

[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] F. Petit, Quelques extensions de la loi de l'arcsinus, C. R. Acad. Sci. Sér. I 315 (1992) 855-858. | MR | Zbl

[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] F. Petit, M. Yor, Itô's formula and the marginals of certain submartingales, Journées sur les Mathématiques financières (1998) 164-167.

[41] J.W. Pitman, 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. | MR | Zbl

[42] J.W. Pitman, M. Yor, A decomposition of Bessel Bridges, Z. Wahr. Verw. Geb 59 (1982) 425-457. | MR | Zbl

[43] J.W. Pitman, M. Yor, 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. | Numdam | MR | Zbl

[44] J.W. Pitman, M. Yor, 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] J.W. Pitman, M. Yor, Laplace transforms related to excursions of a one-dimensional diffusion, Bernoulli 5 (2) (1999) 249-255. | MR | Zbl

[46] B. Rauscher, Some remarks on Pitman's theorem, in: Sém. Probab. XXXI, Lect. Notes Math, vol. 1655, Springer, Berlin, 1997, pp. 266-271. | Numdam | MR | Zbl

[47] D. Revuz, M. Yor, Continuous Martingales and Brownian Motion, Springer, Berlin, 1999. | MR | Zbl

[48] K. Takaoka, 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. | Numdam | MR | Zbl

[49] M. Yor, On square-root boundaries for Bessel processes, and pole-seeking Brownian motion, in: Truman A., Williams D. (Eds.), Stochastic Analysis and Applications, Lect. Notes Math, vol. 1095, Springer, Berlin, 1984. | MR | Zbl

[50] M. Yor, Some Aspects of Brownian Motion. Part I: Some Special Functionals, in: Lect. Math, Birkhaüser, ETH Zürich, 1992. | MR | Zbl

[51] M. Yor, Random Brownian scaling and some absolute continuity relationships, in: Prog. Probab, vol. 36, Birkhaüser, 1995, pp. 243-252. | MR | Zbl

[52] M. Yor, Some Aspects of Brownian Motion. Part II: Some Recent Martingale Problems, in: Lect. Math, Birkhaüser, ETH Zürich, 1997. | MR | Zbl

[53] M. Yor, 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. | Numdam | MR | Zbl

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