The distribution of local times of a brownian bridge
Pitman, Jim
Séminaire de probabilités de Strasbourg, Tome 33 (1999), p. 388-394 / Harvested from Numdam
Access to full text
Full (PDF)
Full (DJVU) 
@article{SPS_1999__33__388_0,
     author = {Pitman, Jim},
     title = {The distribution of local times of a brownian bridge},
     journal = {S\'eminaire de probabilit\'es de Strasbourg},
     volume = {33},
     year = {1999},
     pages = {388-394},
     mrnumber = {1768012},
     zbl = {0945.60081},
     language = {en},
     url = {http://dml.mathdoc.fr/item/SPS_1999__33__388_0}
}

Pitman, Jim. The distribution of local times of a brownian bridge. Séminaire de probabilités de Strasbourg, Tome 33 (1999) pp. 388-394. http://gdmltest.u-ga.fr/item/SPS_1999__33__388_0/

[1] D. Aldous and J. Pitman. Brownian bridge asymptotics for random mappings. Random Structures and Algorithms, 5:487-512, 1994. | MR 1293075 | Zbl 0811.60057

[2] D.J. Aldous and J. Pitman. The standard additive coalescent. Technical Report 489, Dept. Statistics, U.C. Berkeley, 1997. To appear in Ann. Probab.. Available via http://www.stat.berkeley.edu/users/pitman. | MR 1675063 | Zbl 0936.60064

[3] D.J. Aldous and J. Pitman. Tree-valued Markov chains derived from Galton-Vatson processes. Ann. Inst. Henri Poincaré, 34:637-686, 1998. | Numdam | MR 1641670 | Zbl 0917.60082

[4] R.F. Bass and D. Khoshnevisan. Laws of the iterated logarithm for local times of the empirical process. Ann. Probab., 23:388 - 399, 1995. | MR 1330775 | Zbl 0845.60079

[5] J. Bertoin and J. Pitman. Path transformations connecting Brownian bridge, excursion and meander. Bull. Sci. Math. (2), 118:147-166, 1994. | MR 1268525 | Zbl 0805.60076

[6] Ph. Biane and M. Yor. Sur la loi des temps locaux Browniens pris en un temps exponentiel. In Séminaire de Probabilités XXII, pages 454-466. Springer, 1988. Lecture Notes in Math. 1321. | Numdam | MR 960541 | Zbl 0652.60081

[7] A.N. Borodin. Brownian local time. Russian Math. Surveys, 44:2:1-51, 1989. | MR 998360 | Zbl 0705.60064

[8] K.L. Chung. Excursions in Brownian motion. Arkiv fur Matematik, 14:155-177, 1976. | MR 467948 | Zbl 0356.60033

[9] S.N. Evans and J. Pitman. Stopped Markov chains with stationary occupation times. Probab. Th. Rel. Fields, 109:425-433, 1997. | MR 1481128 | Zbl 0888.60058

[10] P. Fitzsimmons, J. Pitman, and M. Yor. Markovian bridges: construction, Palm interpretation, and splicing. In E. Çinlar, K.L. Chung, and M.J. Sharpe, editors, Seminar on Stochastic Processes, 1992, pages 101-134. Birkhäuser, Boston, 1993. | MR 1278079 | Zbl 0844.60054

[11] P. Howard and K. Zumbrun. Invariance of the occupation time of the Brownian bridge process. Preprint, Indiana Univerity. Available via http://www.math.indiana.edu/home/zumbrun, 1998. | MR 1665788

[12] J.P. Imhof. On Brownian bridge and excursion. Studia Sci. Math. Hungar., 20:1-10, 1985. | MR 885996 | Zbl 0625.60096

[13] N.N. Lebedev. Special Functions and their Applications. Prentice-Hall, Englewood Cliffs, N.J., 1965. | MR 174795 | Zbl 0131.07002

[14] C. Leuridan. Le théorème de Ray-Knight à temps fixe. In J. Azéma, M. Émery, M. Ledoux, and M. Yor, editors, Séminaire de Probabilités XXXII, pages 376-406. Springer, 1998. Lecture Notes in Math. 1686. | Numdam | MR 1655305 | Zbl 0919.60073

[15] P. Lévy. Sur certains processus stochastiques homogènes. Compositio Math., 7:283-339, 1939. | JFM 65.1346.02 | Numdam | MR 919 | Zbl 0022.05903

[16] J. Pitman. Cyclically stationary Brownian local time processes. Probab. Th. Rel. Fields, 106:299-329, 1996. | MR 1418842 | Zbl 0857.60074

[17] J. Pitman. The SDE solved by local times of a Brownian excursion or bridge derived from the height profile of a random tree or forest. Technical Report 503, Dept. Statistics, U.C. Berkeley, 1997. To appear in Ann. Prob.. Available via http://www.stat.berkeley.edu/users/pitman. | MR 1681110 | Zbl 0954.60060

[18] J. Pitman and M. Yor. Some properties of the arc sine law related to its invariance under a family of rational maps. In preparation, 1998.

[19] D.B. Ray. Sojourn times of a diffusion process. Ill. J. Math., 7:615-630. 1963. | MR 156383 | Zbl 0118.13403

[20] D. Revuz and M. Yor. Continuous martingales and Brownian motion. Springer, Berlin-Heidelberg, 1994. 2nd edition. | MR 1303781 | Zbl 0804.60001

[21] G.R. Shorack and J.A. Wellner. Empirical processes with applications to statistics. John Wiley & Sons, New York, 1986.

[22] S.S. Wilks. Certain generalizations in the analysis of variance. Biometrika, 24:471-494, 1932. | JFM 58.1172.02 | Zbl 0006.02301

[23] D. Williams. Path decomposition and continuity of local time for one dimensional diffusions I. Proc. London Math. Soc. (3), 28:738-768, 1974. | MR 350881 | Zbl 0326.60093