A parallel between Brownian bridges and Gamma bridges

Publications of the Research Institute for Mathematical Sciences

Volumn 40, Issue 3, 2004, Pages 669-688

  Émery, Michel ^a   Yor, Marc ^b  

^a UNIVERSITÉ LOUIS PASTEUR   (France)

^b SORBONNE UNIVERSITÉ   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 9544228302     PISSN: 00345318     EISSN: 16634926     Source Type: Journal    
DOI: 10.2977/prims/1145475488     Document Type: Article

References (19)

1. Bertoin, J., Subordinators: Examples and Applications, Lectures on Probability and Statistics, Ecole d'Eté de Probabilités de Saint-Flour XXVII-1997, Springer LNM, 1717 (1999).
2. _, Applications de la théorie spectrale des cordes vibrantes aux fonctionnelles additives principales d'un mouvement brownien réfléchi, Ann. Inst. H. Poincaré Probab. Statist, 25 (1989), 307-323.
3. Biane, P. and Yor, M., Valeurs principales associées aux temps locaux browniens, Bull. Sci. Math., 111 (1987), 23-101.
4. Chaumont, L. and Yor, M., Exercises in Probability, Cambridge Univ. Press, 2003.
5. Diaconis, P. and Kemperman, J., Some new tools for Dirichlet priors, Bayesian Statistics 5, J. M. Bernardo, J. O. Berger, A. P. Dawid and A. F. M. Smith eds., 97-106. Oxford University Press, 1996.
6. Ferguson, T. S., A Bayesian analysis of some nonparametric problems, Ann. Stat., 1 (1973), 209-230.
7. Hammersley, J. M., Harnesses, Proc. Fifth Berkeley Sympos. Mathematical Statistics and Probability, Vol. III: Physical Sciences., Univ. California Press, Berkeley, 89-117, 1967.
8. Jacod, J., Calcul stochastique et problèmes de martingales, Springer LNM, 714 (1979).
9. Jacod, J. and Protter, P., Time reversal on Levy processes, Ann. Prob., 16 (1988), 620-641.
10. Jeulin, T. and Yor, M., Filtration des ponts browniens et équations différentielles linéaires, Séminaire de Probabilités XXIV, 227-265, Springer LNM, 1426 (1990).
11. Knight, F.B., Characterization of the Lévy measures of inverse local times of gap diffusion, Seminar on Stochastic Processes, 1981., Prog. Prob. Statist., 1 53-78, Birkhäuser 1981.
12. Kotani, S. and Watanabe, S., Kreǐn's spectral theory of strings and generalized diffusion processes, Functional analysis in Markov processes (Katata/Kyoto 1981), Springer LNM, 923 (1982), 235-259.
13. Lukacs, E., A characterization of the gamma distribution, Ann. Math. Stat., 26 (1965), 319-324.
14. Pitman, J. and Yor, M., Arcsine laws and interval partitions derived from a stable subordinator, Proc. London Math. Soc., 65 (1992), 326-356.
15. Tsilevich, N. and Vershik, A., Quasi-invariance of the gamma process and multiplicative properties of the Poisson-Dirichlet measures, C. R. Acad. Sci. Paris Sér. I, 329 (1999), 163-168.
16. Tsilevich, N., Vershik, A. and Yor, M., An infinite dimensional analogue of the Lebesgue measure and distinguished properties of the gamma process, J. Fund. Anal., 185 (2001), 274-296.
17. Vershik, A. and Yor, M., Multiplicativité du processus gamma et étude asymptotique des lois stables d'indice α, lorsque α tends vers 0. Prépubl. 289, Laboratoire de Probabilités, Paris, 1995.
18. Williams, D., Some basic theorems on harnesses, Stochastic Analysis (a tribute to the memory of Rollo Davidson), D. Kendall and H. Harding eds. Wiley, 1973.
19. Yor, M., Some Aspects of Brownian Motion. Part I: Some Special Functional, Lectures Math. ETH Zürich, Birkhäuser 1992.