Laplace transforms related to excursions of a one-dimensional diffusion

Bernoulli

Volumn 5, Issue 2, 1999, Pages 249-255

  Pitman, Jim ^a   Marc, Yor ^b  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b University of Paris VII LPSM partially supported by ERC Starting Grant 680275 MALIG   (France)

Author keywords

Brownion motion; Hyperbolic function; Local time

Indexed keywords

EID: 0007433243     PISSN: 13507265     EISSN: None     Source Type: Journal    
DOI: 10.2307/3318434     Document Type: Article

References (15)

1. Borodin, A. and Salminen, P. (1996) Handbook of Brownian Motion - Facts and Formulae. Boston, MA: Birkhäuser.
2. Greenwood, P. and Pitman, J. (1980) Fluctuation identities for Levy processes and splitting at the maximum. Adv. Appl. Probab., 12, 893-902.
3. Itô, K. (1971) Poisson point processes attached to Markov processes. Proceedings of the Sixth Berkeley Symposium on Mathematical Statistics and Probability, Vol. 3, pp. 225-240. Berkeley, CA: University of California Press.
4. Itô, K. and McKean, H. (1965) Diffusion Processes and their Sample Paths. Berlin: Springer-Verlag.
5. Jeanblanc, M., Pitman, J. and Vor, M. (1997) The Feynman-Kac formula and decomposition of Brownian paths. Comput. Appl. Math., 16, 27-52.
6. Knight, F. (1969) Brownian local times and taboo processes. Trans. Amer. Math. Soc., 143, 173-185.
7. Knight, F. (1978) On sojourn times of killed Brownian motion. In Séminaire de Probabilités XII, pp. 428-445. Lecture Notes in Math. 649. Berlin: Springer-Verlag.
8. Knight, F. (1981) Characterization of the Lévy measure of inverse local times of gap diffusions. Seminar on Stochastic Processes, 1981, pp. 53-78. Boston, MA: Birkhäuser.
9. Kotani, S. and Watanabe, S. (1982) Krein's spectral theory of strings and generalized diffusion processes. In M. Fukushima (ed.) Functional Analysis in Markov Processes, pp. 235-249. Lecture Notes in Math. 923. Berlin: Springer-Verlag.
10. Pitman, J. (1996) Cyclically stationary Brownian local time processes. Probab. Theory Related Fields, 106, 299-329.
11. Pitman, J. and Yor, M. (1986) Asymptotic laws of planar Brownian motion. Ann. Probab., 14, 733-779.
12. Rogers, L. and Williams, D. (1987) Diffusions, Markov Processes and Martingales. New York: Wiley.
13. Taylor, H.M. (1975) A stopped Brownian motion formula. Ann. Probab., 3, 234-246.
14. Williams, D. (1974) Path decomposition and continuity of local time for one dimensional diffusions I. Proc. London Math. Soc., Third Ser., 28, 738-768.
15. Williams, D. (1976) On a stopped Brownian motion formula of H.M. Taylor. In Séminaire de Probabilités X, pp. 235-239. Lecture Notes in Math. 511. Berlin: Springer-Verlag.