Abel transform and integrals of Bessel local times
Annales de l'I.H.P. Probabilités et statistiques, Volume 35 (1999) no. 4, p. 531-572
@article{AIHPB_1999__35_4_531_0,
     author = {Gradinaru, Mihai and Roynette, Bernard and Vallois, Pierre and Yor, Marc},
     title = {Abel transform and integrals of Bessel local times},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     publisher = {Gauthier-Villars},
     volume = {35},
     number = {4},
     year = {1999},
     pages = {531-572},
     zbl = {0937.60080},
     mrnumber = {1702241},
     language = {en},
     url = {http://www.numdam.org/item/AIHPB_1999__35_4_531_0}
}
Gradinaru, Mihai; Roynette, Bernard; Vallois, Pierre; Yor, Marc. Abel transform and integrals of Bessel local times. Annales de l'I.H.P. Probabilités et statistiques, Volume 35 (1999) no. 4, pp. 531-572. http://www.numdam.org/item/AIHPB_1999__35_4_531_0/

[1] J. Azéma, Quelques applications de la théorie générale des processus, Invent. Math. 18 (1972) 293-336. | MR 326848 | Zbl 0268.60068

[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. | Numdam | MR 544782 | Zbl 0414.60055

[3] M. Baxter and D. Williams, Symmetry characterizations of certain distributions 1, Math. Proc. Camb. Phil. Soc. 111 (1992) 387-399. | MR 1142757 | Zbl 0756.60076

[4] M. Baxter and D. Williams, Symmetry characterizations of certain distributions 2, Math. Proc. Camb. Phil. Soc. 112 (1992) 599-611. | MR 1178009 | Zbl 0777.60013

[5] J. Bertoin and M. Yor, Some independence results related to the arcsine law, J. Theor. Probab. 9 (1996) 447-458. | MR 1385407 | Zbl 0876.60060

[6] A.N. Borodin and P. Salminen, Handbook of Brownian Motion: Facts and Formulae, Birlehäuser, Berlin, 1996. | MR 1477407 | Zbl 0859.60001

[7] D.A. Darling and M. Kac, On occupation times for Markov processes, Trans. Amer. Math. Soc. 84 (1957) 444-458. | MR 84222 | Zbl 0078.32005

[8] R.K. Getoor, The Brownian escape process, Ann. Probab. 7 (1979) 864-867. | MR 542136 | Zbl 0416.60086

[9] R. Gorenflo and S. Vessella, Abel Integral Equations: Analysis and Applications, Lect. Notes Math., Vol. 1461, Springer, Berlin, 1991. | MR 1095269 | Zbl 0717.45002

[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. | MR 1993869 | Zbl 1123.60065

[11] K. Ito and H.P. Mckean, Diffusion Processes and Their Sample Paths, Springer, Berlin, 1965. | Zbl 0127.09503

[12] Th. Jeulin, Semi-martingales et Grossissement d'une Filtration, Lect. Notes Math., Vol. 833, Springer, Berlin, 1980. | MR 604176 | Zbl 0444.60002

[13] J. Kent, Some probabilistic properties of Bessel functions, Ann. Probab. 6 (1978) 760-770. | MR 501378 | Zbl 0402.60080

[14] S.A. Molchanov and E. Ostrovskii, Symmetric stable processes as traces of degenerate diffusion processes, Theoty Probab. Appl. 14 (1969) 128-131. | MR 247668 | Zbl 0281.60091

[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. | MR 620995 | Zbl 0469.60076

[16] B. Rajeev and M. Yor, Local times and almost sure convergence of semimartingales, Ann. Inst. Henri Poincaré 31 (1995) 653-667. | Numdam | MR 1355611 | Zbl 0834.60047

[17] D. Revuz and M. Yor, Continuous Martingales and Brownian Motion, 2nd Ed., Springer, Berlin, 1994. | MR 1303781 | Zbl 0804.60001

[18] M.J. Sharpe, Some transformations of diffusions by time reversal, Ann. Probab. 8 (1980) 1157-1162. | MR 602388 | Zbl 0465.60066

[19] S. Sato and M. Yor, Computations of moments for discounted Brownian additive functionals, J. Math. Kyoto 38 (3) (1998) 475-486. | MR 1661228 | Zbl 0943.60068

[20] M. Yor, Some Aspects of Brownian Motion I: Some Special Functionals, Birkhäuser, Basel, 1992. | MR 1193919 | Zbl 0779.60070

[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. | MR 1442263 | Zbl 0880.60082

[23] M. Yor, On certain discounted arcsine laws, Stochastic Process. Appl. 71 (1997) 111-122. | MR 1480642 | Zbl 0943.60069