Download this PDF file Fullscreen Fullscreen Off
References
- Aldous, David; Pitman, Jim. The standard additive coalescent. Ann. Probab. 26 (1998), no. 4, 1703--1726. MR1675063
- sc L. Alili, L. Chaumont and R.A. Doney (2003). On a fluctuation identity for random walks and Lévy processes. Pré-publication No 837 du Laboratoire de Probabilités et Modèles Aléatoires.
- Bertoin, Jean. A fragmentation process connected to Brownian motion. Probab. Theory Related Fields 117 (2000), no. 2, 289--301. MR1771665
- Biane, Ph. Relations entre pont et excursion du mouvement brownien réel. (French) [Relations between Brownian bridge and excursion] Ann. Inst. H. Poincaré Probab. Statist. 22 (1986), no. 1, 1--7. MR0838369
- Biane, Ph.; Yor, M. Quelques précisions sur le méandre brownien. (French) [Some refinements of results on the Brownian meander] Bull. Sci. Math. (2) 112 (1988), no. 1, 101--109. MR0942801
- Chassaing, Philippe; Janson, Svante. A Vervaat-like path transformation for the reflected Brownian bridge conditioned on its local time at 0. Ann. Probab. 29 (2001), no. 4, 1755--1779. MR1880241
- Chaumont, L. An extension of Vervaat's transformation and its consequences. J. Theoret. Probab. 13 (2000), no. 1, 259--277. MR1744984
- Durrett, Richard T.; Iglehart, Donald L. Functionals of Brownian meander and Brownian excursion. Ann. Probability 5 (1977), no. 1, 130--135. MR0436354
- Dvoretzky, A.; Motzkin, Th. A problem of arrangements. Duke Math. J. 14, (1947). 305--313. MR0021531
- Feller, William. An introduction to probability theory and its applications. Vol. II. Second edition John Wiley & Sons, Inc., New York-London-Sydney 1971 xxiv+669 pp. MR0270403
- Fristedt, Bert; Taylor, S. J. Constructions of local time for a Markov process. Z. Wahrsch. Verw. Gebiete 62 (1983), no. 1, 73--112. MR0684210
- Iglehart, Donald L. Random walks with negative drift conditioned to stay positive. J. Appl. Probability 11 (1974), 742--751. MR0368168
- Imhof, J.-P. Density factorizations for Brownian motion, meander and the three-dimensional Bessel process, and applications. J. Appl. Probab. 21 (1984), no. 3, 500--510. MR0752015
- Imhof, J.-P. On Brownian bridge and excursion. Studia Sci. Math. Hungar. 20 (1985), no. 1-4, 1--10. MR0885996
- Kiefer, J. $K$-sample analogues of the Kolmogorov-Smirnov and Cramér-V. Mises tests. Ann. Math. Statist. 30 1959 420--447. MR0102882
- Lévy, Paul. Processus stochastiques et mouvement brownien. (French) Suivi d'une note de M. Loève. Deuxième édition revue et augmentée Gauthier-Villars & Cie, Paris 1965 vi+438 pp. MR0190953
- Liggett, Thomas M. An invariance principle for conditioned sums of independent random variables. J. Math. Mech. 18 1968 559--570. MR0238373
- Miermont, Grégory. Ordered additive coalescent and fragmentations associated to Levy processes with no positive jumps. Electron. J. Probab. 6 (2001), no. 14, 33 pp. (electronic). MR1844511 http://math.washington.edu/~ejpecp/ejp6contents.html
- Pitman, J. Combinatorial stochastic processes. Lectures from the 32nd Summer School on Probability Theory held in Saint-Flour, July 7–24, 2002. With a foreword by Jean Picard. Lecture Notes in Mathematics, 1875. Springer-Verlag, Berlin, 2006. x+256 pp. ISBN: 978-3-540-30990-1; 3-540-30990-X MR2245368 http://stat-www.berkeley.edu
- Pitman, Jim; Yor, Marc. Decomposition at the maximum for excursions and bridges of one-dimensional diffusions. Itô's stochastic calculus and probability theory, 293--310, Springer, Tokyo, 1996. MR1439532
- Pitman, Jim; Yor, Marc. The law of the maximum of a Bessel bridge. Electron. J. Probab. 4 (1999), no. 15, 35 pp. (electronic). MR1701890
- Schweinsberg, Jason. Applications of the continuous-time ballot theorem to Brownian motion and related processes. Stochastic Process. Appl. 95 (2001), no. 1, 151--176. MR1847096
- Vervaat, Wim. A relation between Brownian bridge and Brownian excursion. Ann. Probab. 7 (1979), no. 1, 143--149. MR0515820

This work is licensed under a Creative Commons Attribution 3.0 License.