Properties of perpetual integral functionals of brownian motion with drift
Salminen, Paavo ; Yor, Marc
Annales de l'I.H.P. Probabilités et statistiques, Tome 41 (2005), p. 335-347 / Harvested from Numdam
@article{AIHPB_2005__41_3_335_0,
     author = {Salminen, Paavo and Yor, Marc},
     title = {Properties of perpetual integral functionals of brownian motion with drift},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     volume = {41},
     year = {2005},
     pages = {335-347},
     doi = {10.1016/j.anihpb.2004.01.006},
     mrnumber = {2139023},
     zbl = {1082.60073},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPB_2005__41_3_335_0}
}
Salminen, Paavo; Yor, Marc. Properties of perpetual integral functionals of brownian motion with drift. Annales de l'I.H.P. Probabilités et statistiques, Tome 41 (2005) pp. 335-347. doi : 10.1016/j.anihpb.2004.01.006. http://gdmltest.u-ga.fr/item/AIHPB_2005__41_3_335_0/

[1] J. Bertoin, Subordinators: Examples and applications, in: Bertoin J., Martinelli F., Peres Y. (Eds.), École d'eté de Probabilités de Saint-Flour XXVII-1997, Lecture Notes in Math., vol. 1717, Springer, Berlin, 1999, pp. 1-91. | MR 1746300 | Zbl 0955.60046

[2] A.N. Borodin, P. Salminen, Handbook of Brownian Motion - Facts and Formulae, Birkhäuser, Basel, 2002. | MR 1912205 | Zbl 1012.60003

[3] A.S. Cherny, Convergence of some integrals associated with Bessel processes, Theoret. Probab. Appl. 45 (2000) 251-267. | MR 1967756 | Zbl 0982.60077

[4] K.L. Chung, Z. Zhao, From Brownian Motion to Schrödinger's Equation, Springer-Verlag, Berlin, 1995. | MR 1329992 | Zbl 0819.60068

[5] M. Csörgö, L. Horváth, Q.M. Shao, Convergence of integrals of uniform empirical and quantile processes, Stochastic Process. Appl. 45 (1993) 278-294. | MR 1208874 | Zbl 0784.60038

[6] C. Dellacherie, P.A. Meyer, Probabilités et Potentiel, vols. I-V, Hermann, Paris, 1975. | MR 488194 | Zbl 0323.60039

[7] D. Dufresne, The distribution of a perpetuity, with applications to risk theory and pension funding, Scand. Actuar. J. 1-2 (1990) 39-79. | MR 1129194 | Zbl 0743.62101

[8] R. Durrett, Brownian Motion and Martingales in Analysis, Wadsworth, Belmont, CA, 1984. | MR 750829 | Zbl 0554.60075

[9] M. Emery, Une définition faible de BMO, Ann. Inst. H. Poincare 21 (1985) 59-72. | Numdam | MR 791270 | Zbl 0611.60043

[10] H.J. Engelbert, W. Schmidt, On the behaviour of certain functionals of the Wiener process and applications to stochastic differential equations, in: Stochastic Differential Systems. Proc. 3rd IFIP-WG 7/1 Working Conf., Lecture Notes in Control and Inform. Sci., vol. 36, Springer-Verlag, Berlin, 1981, pp. 47-55. | MR 653645 | Zbl 0468.60077

[11] H.J. Engelbert, W. Schmidt, On exponential local martingales connected with diffusion processes, Math. Nachr. 119 (1984) 97-115. | MR 774179 | Zbl 0565.60063

[12] H.J. Engelbert, W. Schmidt, On the behaviour of certain Bessel functionals. An application to a class of stochastic differential equations, Math. Nachr. 131 (1987) 219-234. | MR 908813 | Zbl 0627.60070

[13] H.J. Engelbert, T. Senf, On functionals of Wiener process with drift and exponential local martingales, in: Dozzi M., Engelbert H.J., Nualart D. (Eds.), Stochastic Processes and Related Topics, Proc. Wintersch. Stochastic Processes, Optim. Control, Georgenthal/Ger. 1990, Math. Res., vol. 61, Academic-Verlag, Berlin, 1991, pp. 45-58. | MR 1127879 | Zbl 0744.60098

[14] P. Fitzsimmons, J. Pitman, Kac's moment formula and the Feynman-Kac formula for additive functionals of a Markov process, Stochastic Process. Appl. 79 (1999) 117-134. | MR 1670526 | Zbl 0962.60067

[15] T. Jeulin, Semimartingales et grossissement d'une filtration, Lecture Notes in Math., vol. 833, Springer-Verlag, Berlin, 1980. | MR 604176 | Zbl 0444.60002

[16] T. Jeulin, Sur la convergence absolue de certaines intégrales, in: Azéma J., Yor M. (Eds.), Séminaire de Probabilités XVI, Lecture Notes in Math., vol. 920, Springer, Berlin, 1982, pp. 248-256. | Numdam | MR 658688 | Zbl 0483.60020

[17] N. Kazamaki, Continuous Exponential Martigales and BMO, Lecture Notes in Math., vol. 1579, Springer-Verlag, Berlin, 1994. | MR 1299529 | Zbl 0806.60033

[18] N. Kazamaki, T. Sekiguchi, On the transformation of some classes of martingales by a change of law, Tôhoku Math. J. 31 (1979) 261-279. | MR 547641 | Zbl 0438.60040

[19] R. Khas'Minskii, On positive solutions of the equation Au+Vu=0, Theoret. Probab. Appl. 4 (1959) 309-318. | Zbl 0089.34501

[20] P.A. Meyer, Probabilités et potential, Hermann (Editions Scientifiques), Paris, 1966. | MR 205287

[21] J. Pitman, M. Yor, Bessel processes and infinitely divisible laws, in: Williams D. (Ed.), Stochastic Integrals, Lecture Notes in Math., vol. 851, Springer-Verlag, Berlin, 1981, pp. 285-370. | MR 620995 | Zbl 0469.60076

[22] J. Pitman, M. Yor, A decomposition of Bessel bridges, Z. Wahrsch. Verw. Gebiete 59 (1982) 425-457. | MR 656509 | Zbl 0484.60062

[23] J. Pitman, M. Yor, Some divergent integrals of Brownian motion, Adv. Appl. Probab. (Supplement) (1986) 109-116. | MR 868512 | Zbl 0618.60074

[24] P. Salminen, M. Yor, Perpetual integral functionals as hitting times, Elec. J. Prob., in press.

[25] L.A. Shepp, Radon-Nikodym derivatives of Gaussian measures, Ann. Math. Statist. 37 (1966) 321-354. | MR 190999 | Zbl 0142.13901

[26] B. Simon, Functional Integration and Quantum Physics, Academic Press, New York, 1979. | MR 544188 | Zbl 0434.28013

[27] W. Stummer, K.-T. Sturm, On exponentials of additive functionals of Markov processes, Stochastic Process. Appl. 85 (2000) 45-60. | MR 1730619 | Zbl 0996.60090

[28] X.-X. Xue, A zero-one law for integral functionals of the Bessel process, in: Azéma J., Meyer P.A., Yor M. (Eds.), Séminaire de Probabilités XXIV, Lecture Notes in Math., vol. 1426, Springer, Berlin, 1990, pp. 137-153. | Numdam | MR 1071537 | Zbl 0704.60082

[29] M. Yor, Sur certaines fonctionnelles exponentielles du mouvement brownien réel, J. Appl. Probab. 29 (1992) 202-208. | MR 1147781 | Zbl 0758.60085

[30] M. Yor, Exponential Functionals of Brownian Motion and Related Processes, Springer Finance, Springer-Verlag, Berlin, 2001. | MR 1854494 | Zbl 0999.60004