Abel transform and integrals of Bessel local times
Mihai Gradinaru; Bernard Roynette; Pierre Vallois; Marc Yor
Annales de l'I.H.P. Probabilités et statistiques (1999)
- Volume: 35, Issue: 4, page 531-572
- ISSN: 0246-0203
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topGradinaru, Mihai, et al. "Abel transform and integrals of Bessel local times." Annales de l'I.H.P. Probabilités et statistiques 35.4 (1999): 531-572. <http://eudml.org/doc/77639>.
@article{Gradinaru1999,
author = {Gradinaru, Mihai, Roynette, Bernard, Vallois, Pierre, Yor, Marc},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {Bessel processes; local time; Abel transform},
language = {eng},
number = {4},
pages = {531-572},
publisher = {Gauthier-Villars},
title = {Abel transform and integrals of Bessel local times},
url = {http://eudml.org/doc/77639},
volume = {35},
year = {1999},
}
TY - JOUR
AU - Gradinaru, Mihai
AU - Roynette, Bernard
AU - Vallois, Pierre
AU - Yor, Marc
TI - Abel transform and integrals of Bessel local times
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 1999
PB - Gauthier-Villars
VL - 35
IS - 4
SP - 531
EP - 572
LA - eng
KW - Bessel processes; local time; Abel transform
UR - http://eudml.org/doc/77639
ER -
References
top- [1] J. Azéma, Quelques applications de la théorie générale des processus, Invent. Math.18 (1972) 293-336. Zbl0268.60068MR326848
- [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. Zbl0414.60055MR544782
- [3] M. Baxter and D. Williams, Symmetry characterizations of certain distributions 1, Math. Proc. Camb. Phil. Soc.111 (1992) 387-399. Zbl0756.60076MR1142757
- [4] M. Baxter and D. Williams, Symmetry characterizations of certain distributions 2, Math. Proc. Camb. Phil. Soc.112 (1992) 599-611. Zbl0777.60013MR1178009
- [5] J. Bertoin and M. Yor, Some independence results related to the arcsine law, J. Theor. Probab.9 (1996) 447-458. Zbl0876.60060MR1385407
- [6] A.N. Borodin and P. Salminen, Handbook of Brownian Motion: Facts and Formulae, Birlehäuser, Berlin, 1996. Zbl0859.60001MR1477407
- [7] D.A. Darling and M. Kac, On occupation times for Markov processes, Trans. Amer. Math. Soc.84 (1957) 444-458. Zbl0078.32005MR84222
- [8] R.K. Getoor, The Brownian escape process, Ann. Probab.7 (1979) 864-867. Zbl0416.60086MR542136
- [9] R. Gorenflo and S. Vessella, Abel Integral Equations: Analysis and Applications, Lect. Notes Math., Vol. 1461, Springer, Berlin, 1991. Zbl0717.45002MR1095269
- [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. Zbl1123.60065MR1993869
- [11] K. Ito and H.P. Mckean, Diffusion Processes and Their Sample Paths, Springer, Berlin, 1965. Zbl0127.09503
- [12] TH. Jeulin, Semi-martingales et Grossissement d'une Filtration, Lect. Notes Math., Vol. 833, Springer, Berlin, 1980. Zbl0444.60002MR604176
- [13] J. Kent, Some probabilistic properties of Bessel functions, Ann. Probab.6 (1978) 760-770. Zbl0402.60080MR501378
- [14] S.A. Molchanov and E. Ostrovskii, Symmetric stable processes as traces of degenerate diffusion processes, Theoty Probab. Appl.14 (1969) 128-131. Zbl0281.60091MR247668
- [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. Zbl0469.60076MR620995
- [16] B. Rajeev and M. Yor, Local times and almost sure convergence of semimartingales, Ann. Inst. Henri Poincaré31 (1995) 653-667. Zbl0834.60047MR1355611
- [17] D. Revuz and M. Yor, Continuous Martingales and Brownian Motion, 2nd Ed., Springer, Berlin, 1994. Zbl0804.60001MR1303781
- [18] M.J. Sharpe, Some transformations of diffusions by time reversal, Ann. Probab.8 (1980) 1157-1162. Zbl0465.60066MR602388
- [19] S. Sato and M. Yor, Computations of moments for discounted Brownian additive functionals, J. Math. Kyoto38 (3) (1998) 475-486. Zbl0943.60068MR1661228
- [20] M. Yor, Some Aspects of Brownian Motion I: Some Special Functionals, Birkhäuser, Basel, 1992. Zbl0779.60070MR1193919
- [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. Zbl0880.60082MR1442263
- [23] M. Yor, On certain discounted arcsine laws, Stochastic Process. Appl.71 (1997) 111-122. Zbl0943.60069MR1480642
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