Some consequences of the cyclic exchangeability property for exponential functionals of Lévy processes
Séminaire de probabilités de Strasbourg, Tome 35 (2001) , pp. 334-347.
@article{SPS_2001__35__334_0,
     author = {Chaumont, Lo{\"\i}c and Hobson, David G. and Yor, Marc},
     title = {Some consequences of the cyclic exchangeability property for exponential functionals of L\'evy processes},
     journal = {S\'eminaire de probabilit\'es de Strasbourg},
     pages = {334--347},
     publisher = {Springer - Lecture Notes in Mathematics},
     volume = {35},
     year = {2001},
     zbl = {0982.60020},
     mrnumber = {1837296},
     language = {en},
     url = {http://www.numdam.org/item/SPS_2001__35__334_0/}
}
Chaumont, Loïc; Hobson, David G.; Yor, Marc. Some consequences of the cyclic exchangeability property for exponential functionals of Lévy processes. Séminaire de probabilités de Strasbourg, Tome 35 (2001) , pp. 334-347. http://www.numdam.org/item/SPS_2001__35__334_0/

[1] D.J. Aldous: Exchangeability and related topics. Lecture notes in Math., Springer, vol. 1117 École d'été de Probabilité de Saint-Flour XIII, 1983. | MR 883646 | Zbl 0562.60042

[2] J. Bertoin: Lévy Processes. Cambridge University Press 1996. | MR 1406564 | Zbl 0861.60003

[3] J. Bertoin: Some elements on Lévy Processes Handbook of statistics, Stochastic processes. Theory and methods. D.N.S. Shanbhag, North Holland, to appear (2000). | MR 1861722 | Zbl 0982.60042

[4] J. Bertoin, L. Chaumont and M. Yor: Two chain-transformations and their applications to quantiles. J. Appl. Prob. 34, (1997), 882-897. | MR 1484022 | Zbl 0904.60059

[5] P. Biane: Relations entre pont brownien et excursion renormalisée du mouvement brownien. Ann. Inst. Henri Poincaré 22 (1986), 1-7. | Numdam | MR 838369 | Zbl 0596.60079

[6] P. Carmona, F. Petit, M. Yor: Some extensions of the arc sine law as partial consequences of the scaling property of Brownian motion. Prob. Th. Rel. Fields 100 (1994), no. 1, 1-29. | MR 1292188 | Zbl 0808.60066

[7] L. Chaumont: An extension of Vervaat's transformation and its consequences. J. Theor. Prob., vol. 13, n° 1, p. 259-278 (2000). | MR 1744984 | Zbl 0952.60079

[8] A. Dassios: Sample quantiles of stochastic processes with stationary and independent increments and of sums of exchangeable random variables. Ann. App. Probab. vol. 6, No. 3, (1996), 1041-1043. | MR 1410129 | Zbl 0860.60025

[9] L.E. Dubins, J. Pitman: A pointwise ergodic theorem for the group of rational rotations. Trans. Amer. Math. Soc. 251, 299-308, 1980. | MR 531981 | Zbl 0412.60050

[10] C. Donati-Martin, H. Matsumoto, M. Yor: The law of geometric Brownian motion and its integral, revisited; application to conditional moments. Preprint (2000). | MR 1960566

[11] C. Donati-Martin, H. Matsumoto, M. Yor: On a striking identity about the exponential functional of the Brownian bridge. To appear in Periodica Math. Hung., (2001). | Zbl 01604378

[12] P.J. Fitzsimmons and R.K. Getoor: Occupation time distributions for Lévy bridges and excursions. Stoch. Proc. Appl. 58, (1995), 73-89. | MR 1341555 | Zbl 0837.60071

[13] P.J. Fitzsimmons, J. Pitman and M. Yor: Markovian bridges: construction, Palm interpretation, and splicing. Seminar on Stochastic Processes, 1992 (Seattle, WA, 1992), 101-134, Progr. Probab., 33, Birkhäuser Boston, Boston, MA, 1993. | MR 1278079 | Zbl 0844.60054

[14] O. Kallenberg: Canonical representation and convergence criteria for processes with interchangeable increments. Zeit. Whahr. verw. Geb. 27, 23-36, 1973. | MR 394842 | Zbl 0253.60060

[15] F.B. Knight: The uniform law for exchangeable and Lévy process bridges. Hommage a P. A. Meyer et J. Neveu, Astérisque, (1996), 171-188. | MR 1417982 | Zbl 0867.60018

[16] F.S. Nasyrov: On local times for functions and stochastic processes I. Theory Probab. Appl. Vol. 40, No. 4, (1995), 702-713. | MR 1405146 | Zbl 0909.60057

[17] D. Revuz and M. Yor: Continuous martingales and Brownian motion, Springer, Berlin, Third edition, (1999). | MR 1725357 | Zbl 0917.60006

[18] W. Vervaat: A relation between Brownian bridge and Brownian excursion. Ann. Probab. 7 (1979), 141-149. | MR 515820 | Zbl 0392.60058

[19] M. Yor: The distribution of Brownian quantiles. J. Appl. Prob. 32, (1995),405-416. | MR 1334895 | Zbl 0829.60065