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 Electronic Communications in Probability > Vol. 4 (1999) > Paper 5 open journal systems 


Construction of a Brownian Path With a Given Minimum

Jean Bertoin, Universite Pierre et Marie Curie
Jim Pitman, University of California, Berkeley
Juan Ruiz de Chavez, UAM-I


Abstract
We construct a Brownian path conditioned on its minimum value over a fixed time interval by a simple transformation of a Brownian bridge.


Full text: PDF

Pages: 31-37

Published on: July 9, 1999
Bibliography
  1. S. Asmussen, P. Glynn, and J. Pitman. Discretization error in simulation of one-dimensional reflecting Brownian motion. Ann. Applied Prob. , 5:875--896, 1995. Math. Review 97e:65156.
  2. J. Bertoin. Décomposition du mouvement brownien avec dérive en un minimum local par juxtaposition de ses excursions positives et negatives. In Séminaire de Probabilités XXV, pages 330-344. Springer-Verlag, 1991. Lecture Notes in Math. 1485. Math. Review 93k:60204.
  3. J. Bertoin and J. Pitman. Path transformations connecting Brownian bridge, excursion and meander. Bull. Sci. Math. (2), 118:147-166, 1994. Math. Review 95b:60097.
  4. Ph. Biane. Relations entre pont et excursion du mouvement brownien réel. Ann. Inst. Henri Poincaré,, 22:1-7, 1986. Math. Review 87k:60186.
  5. Ph. Biane and M. Yor. Valeurs principales associées aux temps locaux browniens. Bull. Sci. Math., 111:23-101, 1987. Math. Review 89i:60156.
  6. Ph. Biane and M. Yor. Quelques précisions sur le méandre brownien. Bull. Sci. Math., 112:101-109, 1988. Math. Review 89i:60156.
  7. L. Chaumont. An extension of Vervaat's transformation and its consequences. 1995 (preprint) Math. Review number not available.
  8. K. L. Chung. Excursions in Brownian motion. Arkiv fur Matematik, 14:155-177, 1976. Math. Review 57 #7791.
  9. E. Csáki, A. Földes, and P. Salminen. On the joint distribution of the maximum and its location for a linear diffusion. Ann. Instit. Henri Poincaré, section B, 23:179-194, 1987. Math. Review 88k:60145.
  10. I. V. Denisov. A random walk and a Wiener process near a maximum. Theor. Prob. Appl., 28:821-824, 1984. Math. Review 85f:60117.
  11. W. Feller. An Introduction to Probability Theory and its Applications, Vol 1, 3rd ed. Wiley, New York, 1968. Math. Review 37 #3604.
  12. J. P. Imhof. Density factorizations for Brownian motion, meander and the three-dimensional Bessel process, and applications. J. Appl. Probab., 21:500-510, 1984. Math. Review 85j:60152.
  13. J. P. Imhof. On Brownian bridge and excursion Studia Sci. Math. Hungar., 20:1-10, 1985. Math. Review 88h:60159 .
  14. J. F. Le Gall. Une approche élémentaire des théorèmes de décomposition de Williams. In Séminaire de Probabilités XX, pages 447-464. Springer, 1986. Lecture Notes in Math. 1204. Math. Review 89g:60219 .
  15. J. Pitman. One-dimensional Brownian motion and the three-dimensional Bessel process. Advances in Applied Probability, 7:511-526, 1975. Math. Review 51 #11677.
  16. J. Pitman. The distribution of local times of Brownian bridge. Technical Report 539, Dept. Statistics, U.C. Berkeley, 1998. To appear in Séminaire de Probabilités XXXIII. Available via http://www.stat.berkeley.edu/users/pitman.
  17. J. Pitman and M. Yor. Decomposition at the maximum for excursions and bridges of one-dimensional diffusions. In N. Ikeda, S. Watanabe, M. Fukushima, and H. Kunita, editors,Itô's Stochastic Calculus and Probability Theory, pages 293-310. Springer, 1996. Lecture Notes in Math. 851. Math. Review 98f:60153 .
  18. D. Revuz and M. Yor. Continuous martingales and Brownian motion. Springer, Berlin-Heidelberg, 1999. 3rd edition. Math. Review number not available.
  19. W. Vervaat. A relation between Brownian bridge and Brownian excursion. Ann. Probab., 7:143-149, 1979. Math. Review 80b:60107.
  20. D. Williams. Decomposing the Brownian path. Bull. Amer. Math. Soc., 76:871-873, 1970. Math. Review 41 #2777.
  21. D. Williams. Path decomposition and continuity of local time for one dimensional diffusions I. Proc. London Math. Soc. (3), 28:738-768, 1974. Math. Review 50 #3373.
  22. M. Yor. Local times and Excursions for Brownian Motion: a concise introduction,. volume 1 of Lecciones en Matematicas Postgrado de Matematicas, Facultad de Ciencias, Universidad Central de Venezuela, Caracas, 1995. Math. Review number not available.
















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Electronic Communications in Probability. ISSN: 1083-589X