On the entire moments of self-similar Markov processes and exponential functionals of Lévy processes
Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 11 (2002) no. 1, pp. 33-45.
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     author = {Jean Bertoin and Marc Yor},
     title = {On the entire moments of self-similar {Markov} processes and exponential functionals of {L\'evy} processes},
     journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
     pages = {33--45},
     publisher = {Universit\'e Paul Sabatier. Facult\'e des sciences},
     address = {Toulouse},
     volume = {Ser. 6, 11},
     number = {1},
     year = {2002},
     zbl = {1031.60038},
     mrnumber = {1986381},
     language = {en},
     url = {https://afst.centre-mersenne.org/item/AFST_2002_6_11_1_33_0/}
}
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Jean Bertoin; Marc Yor. On the entire moments of self-similar Markov processes and exponential functionals of Lévy processes. Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 11 (2002) no. 1, pp. 33-45. https://afst.centre-mersenne.org/item/AFST_2002_6_11_1_33_0/

[1] Bertoin (J.). - Lévy Processes, Cambridge University Press, 1996. | MR | Zbl

[2] Bertoin (J.), Biane (Ph.) and Yor (M.). - Poissonian exponential functionals, q-series, q-integrals, and the moment problem for log-normal distributions, to appear in Proceedings Stochastic Analysis, Ascona, Birkhäuser, 2002. | MR | Zbl

[3] Bertoin (J.) and Caballero (M.-E.).- Entrance from 0+ for increasing semi-stable Markov processes, Bernoulli 8 (2002), 195-205. | MR | Zbl

[4] Bertoin (J.) and Yor (M.). - Entrance laws of self-similar Markov processes and exponential functionals of Lévy processes, Potential Analysis 17 (2002), 389-400. | MR | Zbl

[5] Bertoin (J.) and Yor (M.). - On subordinators, self-similar Markov processes, and some factorizations of the exponential law, Elect. Commun. Probab. 6 (2001), 95-106. Available at http://www.math.washington.edu/∼ejpecp/ecpficontents.html. | MR | Zbl

[6] Carmona (P.), Petit (F.) and Yor (M.). - Sur les fonctionnelles exponentielles de certains processus de Lévy, Stochastics and Stochastics Reports 47 (1994), 71-101. | MR | Zbl

[7] Carmona (P.), Petit (F.) and Yor (M.). - On the distribution and asymptotic results for exponential functionals of Lévy process, in: M.Yor (editor) Exponential functionals and principal values related to Brownian Motion, (1997), pp. 73-121. Biblioteca de la Revista Matemática Iberoamericana. | MR | Zbl

[8] Carmona (P.), Petit (F.) and Yor (M.). - Exponential functionals of Lévy processes, O. Barndorff-Nielsen, T. Mikosch and S. Resnick (editors), Lévy processes : theory and applications, (2001), pp. 41-55, Birkhäuser. | MR | Zbl

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

[10] Émery (M.). - On the Azéma martingales, Séminaire de Probabilités XXIII, Lecture Notes in Maths. 1372, Springer, 1989. | Numdam | MR | Zbl

[11] Feller (W.E.). - An introduction to probability theory and its applications, 2nd edn, vol. 2. Wiley, New-York, 1971. | Zbl

[12] Gjessing (H.K.) and Paulsen (J.). - Present value distributions with application to ruin theory and stochastic equations. Stochastic Process. Appl. 71 (1997), 123-144. | MR | Zbl

[13] Hawkes (J.). - On the potential theory of subordinators. Z. Wahrscheinlichkeitstheorie verw. Gebiete 24 (1975), 167-193. | MR | Zbl

[14] Jain (N.C.) and Pruitt (W.E.). - Lower tail probabilities estimates for subordinators and nondecreasing random walks, Ann. Probab. 15 (1987), 75-102. | MR | Zbl

[15] Krein (M.G.). - On an extrapolation problem due to Kolmogorov. Dokl. Akad. Nauk. SSSR 46 (1945), 306-309. | MR | Zbl

[16] Lamperti (J.W.). - Semi-stable Markov processes. Z. Wahrscheinlichkeitstheorie verw. Gebiete 22 (1972), 205-225. | MR | Zbl

[17] Lubensky (D.K.) and Nelson (D.R.).-Single molecule statistics and the polynucleotide unzipping transition, Preprint, 2001. Available at arXiv:cond-mat/0107423v1.

[18] Pakes (A.G.). - Remarks on converse Carleman and Krein criteria for the classical moment problem, J. Austral. Math. Soc. 71 (2001), 81-104. | MR | Zbl

[19] Pedersen (H.L.). - On Krein's theorem for indeterminacy of the classical moment problem, J. Approx. Theor. 95 (1998), 90-100. | MR | Zbl

[20] Pollack (M.) and Siegmund (D.).- A diffusion process and its applications to detecting a change in the drift of Brownian motion, Biometrika 72 (1985), 267-280. | MR | Zbl

[21] Sato (K.-I.). - Lévy processes and infinitely divisible distributions, Cambridge University Press, Cambridge, 1999. | MR | Zbl

[22] Simon (B.). - The classical moment problem as a self adjoint finite difference operator, Adv. in Maths. 137 (1998), 82-203. | MR | Zbl

[23] Stieltjes (T.J.). - Recherches sur les fractions continues. Ann. Fac. Sci. Toulouse 8 (1894-95), 1-122 and 9, 5-47. | JFM | Numdam

[24] Stoyanov (J.). - Krein condition in probabilistic moment problems, Bernoulli 6 (2000), 939-949. | MR | Zbl

[25] Urbanik (K.). - Functionals of transient stochastic processes with independent increments, Studia Math. 103 (3) (1992), 299-315. | MR | Zbl

[26] Williams (D.). - Diffusions, Markov processes, and martingales vol. 1: Foundations, Wiley, New-York, 1979. | MR | Zbl

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

[28] Yor (M.). - Some aspects of Brownian motion, Part II : Some recent martingale problems, Lectures in Mathematics, ETH Zürich, Birkhäuser, 1997. | MR | Zbl

[29] Yor (M.). - Exponential functionals of Brownian motion and related processes, Springer Finance, Berlin, 2001. | MR | Zbl