On the entire moments of self-similar Markov processes and exponential functionals of Lévy processes

 Access to full text

 Full (PDF)

1. [1] Bertoin ( J.). — Lévy Processes, Cambridge University Press, 1996. Zbl0861.60003MR1406564
2. [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. Zbl1056.60046MR2096279
3. [3] Bertoin ( J.) and Caballero ( M.-E.).— Entrance from 0+ for increasing semi-stable Markov processes, Bernoulli8 (2002), 195-205. Zbl1002.60032MR1895890
4. [4] Bertoin ( J.) and Yor ( M.). — Entrance laws of self-similar Markov processes and exponential functionals of Lévy processes, Potential Analysis17 (2002), 389-400. Zbl1004.60046MR1918243
5. [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. Zbl1024.60030MR1871698
6. [6] Carmona ( P.), Petit ( F.) and Yor ( M.). — Sur les fonctionnelles exponentielles de certains processus de Lévy, Stochastics and Stochastics Reports47 (1994), 71-101. Zbl0830.60072MR1787143
7. [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. Zbl0905.60056MR1648657
8. [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. Zbl0979.60038MR1833691
9. [9] Dufresne ( D.). — The distibution of a perpetuity, with applications to risk theory and pension funding, Scand. Actuar. J.1-2 (1990), 39-79. Zbl0743.62101MR1129194
10. [10] Émery ( M.). — On the Azéma martingales, Séminaire de ProbabilitésXXIII, Lecture Notes in Maths.1372, Springer, 1989. Zbl0753.60045MR1022899
11. [11] Feller ( W.E.). — An introduction to probability theory and its applications, 2nd edn, vol. 2. Wiley, New-York, 1971. Zbl0219.60003
12. [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. Zbl0943.60098MR1480643
13. [13] Hawkes ( J.). — On the potential theory of subordinators. Z. Wahrscheinlichkeitstheorie verw. Gebiete24 (1975), 167-193. Zbl0402.60074MR388553
14. [14] Jain ( N.C.) and Pruitt ( W.E.). — Lower tail probabilities estimates for subordinators and nondecreasing random walks, Ann. Probab.15 (1987), 75-102. Zbl0617.60023MR877591
15. [15] Krein ( M.G.). — On an extrapolation problem due to Kolmogorov. Dokl. Akad. Nauk. SSSR46 (1945), 306-309. Zbl0063.03356MR12700
16. [16] Lamperti ( J.W.). — Semi-stable Markov processes. Z. Wahrscheinlichkeitstheorie verw. Gebiete22 (1972), 205-225. Zbl0274.60052MR307358
17. [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. [18] Pakes ( A.G.). — Remarks on converse Carleman and Krein criteria for the classical moment problem, J. Austral. Math. Soc.71 (2001), 81-104. Zbl0992.44003MR1840495
19. [19] Pedersen ( H.L.). — On Krein's theorem for indeterminacy of the classical moment problem, J. Approx. Theor.95 (1998), 90-100. Zbl0924.44009MR1645978
20. [20] Pollack ( M.) and Siegmund ( D.).— A diffusion process and its applications to detecting a change in the drift of Brownian motion, Biometrika72 (1985), 267-280. Zbl0571.60084MR801768
21. [21] Sato ( K.-I.). — Lévy processes and infinitely divisible distributions, Cambridge University Press, Cambridge, 1999. Zbl0973.60001MR1739520
22. [22] Simon ( B.). — The classical moment problem as a self adjoint finite difference operator, Adv. in Maths.137 (1998), 82-203. Zbl0910.44004MR1627806
23. [23] Stieltjes ( T.J.). — Recherches sur les fractions continues. Ann. Fac. Sci. Toulouse8 (1894-95), 1-122 and 9, 5-47. JFM25.0326.01
24. [24] Stoyanov ( J.). — Krein condition in probabilistic moment problems, Bernoulli6 (2000), 939-949. Zbl0971.60017MR1791909
25. [25] Urbanik ( K.). - Functionals of transient stochastic processes with independent increments, Studia Math.103 (3) (1992), 299-315. Zbl0809.60068MR1202015
26. [26] Williams ( D.). - Diffusions, Markov processes, and martingales vol. 1: Foundations, Wiley, New-York, 1979. Zbl0402.60003MR531031
27. [27] Yor ( M.). — Sur certaines fonctionnelles exponentielles du mouvement brownien réel, J. Appl. Probab.29 (1992), 202-208. Zbl0758.60085MR1147781
28. [28] Yor ( M.). — Some aspects of Brownian motion, Part II : Some recent martingale problems, Lectures in Mathematics, ETH Zürich, Birkhäuser, 1997. Zbl0880.60082MR1442263
29. [29] Yor ( M.). — Exponential functionals of Brownian motion and related processes, Springer Finance, Berlin, 2001. Zbl0999.60004MR1854494

1. Patie Pierre, Infinite divisibility of solutions to some self-similar integro-differential equations and exponential functionals of Lévy processes