@article{AFST_2002_6_11_1_33_0, author = {Bertoin, Jean and Yor, Marc}, 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}, mrnumber = {1986381}, zbl = {1031.60038}, language = {en}, url = {http://archive.numdam.org/item/AFST_2002_6_11_1_33_0/} }
TY - JOUR AU - Bertoin, Jean AU - Yor, Marc TI - On the entire moments of self-similar Markov processes and exponential functionals of Lévy processes JO - Annales de la Faculté des sciences de Toulouse : Mathématiques PY - 2002 SP - 33 EP - 45 VL - 11 IS - 1 PB - Université Paul Sabatier. Faculté des sciences PP - Toulouse UR - http://archive.numdam.org/item/AFST_2002_6_11_1_33_0/ LA - en ID - AFST_2002_6_11_1_33_0 ER -
%0 Journal Article %A Bertoin, Jean %A Yor, Marc %T On the entire moments of self-similar Markov processes and exponential functionals of Lévy processes %J Annales de la Faculté des sciences de Toulouse : Mathématiques %D 2002 %P 33-45 %V 11 %N 1 %I Université Paul Sabatier. Faculté des sciences %C Toulouse %U http://archive.numdam.org/item/AFST_2002_6_11_1_33_0/ %G en %F AFST_2002_6_11_1_33_0
Bertoin, Jean; Yor, Marc. 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. http://archive.numdam.org/item/AFST_2002_6_11_1_33_0/
[1] Lévy Processes, Cambridge University Press, 1996. | MR | Zbl
). -[2] 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
), ) and ). -[3] Entrance from 0+ for increasing semi-stable Markov processes, Bernoulli 8 (2002), 195-205. | MR | Zbl
) and ).-[4] Entrance laws of self-similar Markov processes and exponential functionals of Lévy processes, Potential Analysis 17 (2002), 389-400. | MR | Zbl
) and ). -[5] 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
) and ). -[6] Sur les fonctionnelles exponentielles de certains processus de Lévy, Stochastics and Stochastics Reports 47 (1994), 71-101. | MR | Zbl
), ) and ). -[7] 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
), ) and ). -[8] 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
), ) and ). -[9] The distibution of a perpetuity, with applications to risk theory and pension funding, Scand. Actuar. J. 1-2 (1990), 39-79. | MR | Zbl
). -[10] On the Azéma martingales, Séminaire de Probabilités XXIII, Lecture Notes in Maths. 1372, Springer, 1989. | Numdam | MR | Zbl
). -[11] An introduction to probability theory and its applications, 2nd edn, vol. 2. Wiley, New-York, 1971. | Zbl
). -[12] Present value distributions with application to ruin theory and stochastic equations. Stochastic Process. Appl. 71 (1997), 123-144. | MR | Zbl
) and ). -[13] On the potential theory of subordinators. Z. Wahrscheinlichkeitstheorie verw. Gebiete 24 (1975), 167-193. | MR | Zbl
). -[14] Lower tail probabilities estimates for subordinators and nondecreasing random walks, Ann. Probab. 15 (1987), 75-102. | MR | Zbl
) and ). -[15] On an extrapolation problem due to Kolmogorov. Dokl. Akad. Nauk. SSSR 46 (1945), 306-309. | MR | Zbl
). -[16] Semi-stable Markov processes. Z. Wahrscheinlichkeitstheorie verw. Gebiete 22 (1972), 205-225. | MR | Zbl
). -[17] Single molecule statistics and the polynucleotide unzipping transition, Preprint, 2001. Available at arXiv:cond-mat/0107423v1.
) and ).-[18] Remarks on converse Carleman and Krein criteria for the classical moment problem, J. Austral. Math. Soc. 71 (2001), 81-104. | MR | Zbl
). -[19] On Krein's theorem for indeterminacy of the classical moment problem, J. Approx. Theor. 95 (1998), 90-100. | MR | Zbl
). -[20] A diffusion process and its applications to detecting a change in the drift of Brownian motion, Biometrika 72 (1985), 267-280. | MR | Zbl
) and ).-[21] Lévy processes and infinitely divisible distributions, Cambridge University Press, Cambridge, 1999. | MR | Zbl
). -[22] The classical moment problem as a self adjoint finite difference operator, Adv. in Maths. 137 (1998), 82-203. | MR | Zbl
). -[23] Recherches sur les fractions continues. Ann. Fac. Sci. Toulouse 8 (1894-95), 1-122 and 9, 5-47. | JFM | Numdam
). -[24] Krein condition in probabilistic moment problems, Bernoulli 6 (2000), 939-949. | MR | Zbl
). -[25] Functionals of transient stochastic processes with independent increments, Studia Math. 103 (3) (1992), 299-315. | MR | Zbl
). -[26] Diffusions, Markov processes, and martingales vol. 1: Foundations, Wiley, New-York, 1979. | MR | Zbl
). -[27] Sur certaines fonctionnelles exponentielles du mouvement brownien réel, J. Appl. Probab. 29 (1992), 202-208. | MR | Zbl
). -[28] Some aspects of Brownian motion, Part II : Some recent martingale problems, Lectures in Mathematics, ETH Zürich, Birkhäuser, 1997. | MR | Zbl
). -[29] Exponential functionals of Brownian motion and related processes, Springer Finance, Berlin, 2001. | MR | Zbl
). -