Abel transform and integrals of Bessel local times

Annales de l'institut Henri Poincare (B) Probability and Statistics

Volumn 35, Issue 4, 1999, Pages 531-572

  Gradinaru, Mihai ^a   Roynette, Bernard ^a   Vallois, Pierre ^a   Yor, Marc ^b  

^a UNIVERSITÉ HENRI POINCARÉ NANCY 1   (France)

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

Author keywords

Abel's integral operator; Bessel local time

Indexed keywords

EID: 0033163890     PISSN: 02460203     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0246-0203(99)00105-3     Document Type: Article

References (23)

1. J. Azéma, Quelques applications de la théorie générale des processus, Invent. Math. 18 (1972) 293-336.
2. J. Azéma and M. Yor, Une solution simple au problème de Skorokhod, in: C. Dellacherie, P.A. Meyer and M. Weil, eds., Sém. Probab. XIII, Lect. Notes Math., Vol. 721, Berlin, Springer, 1979, pp. 90-115 and 625-633.
3. M. Baxter and D. Williams, Symmetry characterizations of certain distributions 1, Math. Proc. Camb. Phil. Soc. 111 (1992) 387-399.
4. M. Baxter and D. Williams, Symmetry characterizations of certain distributions 2, Math. Proc. Camb. Phil Soc. 112 (1992) 599-611.
5. J. Bertoin and M. Yor, Some independence results related to the arcsine law, J. Theor. Probab. 9 (1996) 447-458.
6. A.N. Borodin and P. Salminen, Handbook of Brownian Motion: Facts and Formulae, Birlehäuser, Berlin, 1996.
7. D.A. Darling and M. Kac, On occupation times for Markov processes, Trans. Amer. Math. Soc. 84 (1957) 444-458.
8. R.K. Getoor, The Brownian escape process, Ann. Probab. 7 (1979) 864-867.
9. R. Gorenflo and S. Vessella, Abel Integral Equations: Analysis and Applications, Lect. Notes Math., Vol. 1461, Springer, Berlin, 1991.
10. M. Gradinaru, B. Roynette, P. Vallois and M. Yor, The laws of Brownian local time integrals, prépublication no. 38-1997, Institut Élie Cartan, Université Henri Poincaré (Vandœuvre-lès-Nancy, France); to appear in Computational and Applied Mathematics, Birkhäuser, Boston, 1999.
11. K. Ito and H.P. McKean, Diffusion Processes and their Sample Paths, Springer, Berlin, 1965.
12. Th. Jeulin, Semi-martingales et Grossissement d'une Filtration, Lect. Notes Math., Vol. 833, Springer, Berlin, 1980.
13. J. Kent, Some probabilistic properties of Bessel functions, Ann. Probab. 6 (1978) 760-770.
14. S.A. Molchanov and E. Ostrovskii, Symmetric stable processes as traces of degenerate diffusion processes, Theoty Probab. Appl. 14 (1969) 128-131.
15. J.W. Pitman and M. Yor, Bessel processes and infinitely divisible laws, in: D. Williams, ed., Stochastic Integrals, Lect. Notes Math., Vol. 851, Springer, Berlin, 1981, pp. 285-370.
16. B. Rajeev and M. Yor, Local times and almost sure convergence of semi-martingales, Ann. Inst. Henri Poincaré 31 (1995) 653-667.
17. D. Revuz and M. Yor, Continuous Martingales and Brownian Motion, 2nd Ed., Springer, Berlin, 1994.
18. M. J. Sharpe, Some transformations of diffusions by time reversal, Ann. Probab. 8 (1980) 1157-1162.
19. S. Sato and M. Yor, Computations of moments for discounted Brownian additive functionals, J. Math. Kyoto 38 (3) (1998) 475-486.
20. M. Yor, Some Aspects of Brownian Motion I: Some Special Functionals, Birkhäuser, Basel, 1992.
21. M. Yor, Local Times and Excursions for Brownian Motion: A Concise Introduction, Caracas-Paris, 1996.
22. M. Yor, Some Aspects of Brownian Motion II: Some Recent Martingale Problems, Birkhäuser, Berlin, 1997.
23. M. Yor, On certain discounted arcsine laws, Stochastic Process. Appl. 71 (1997) 111-122.