Some remarkable properties of gamma processes

Applied and Numerical Harmonic Analysis

Volumn , Issue 9780817645441, 2007, Pages 37-47

  Yor, Marc ^a  

^a SORBONNE UNIVERSITÉ   (France)

Author keywords

Absolute continuity; Bridges; Gamma process; Inverse local time; Time changes

Indexed keywords

EID: 85047403030     PISSN: 22965009     EISSN: 22965017     Source Type: Book Series    
DOI: 10.1007/978-0-8176-4545-8_3     Document Type: Chapter

References (21)

1. D.M. Cifarelli and E. Melilli. Some new results for Dirichlet priors. Ann. Stat., 28:1390–1413, 2000.
2. D.M. Cifarelli and E. Regazzini. Distribution functions of means of a Dirichlet process. Ann. Stat., 18:429–442, 1990.
3. L. Chaumont and M. Yor. Exercises in Probability. Cambridge University Press, 2003.
4. C. Donati-Martin and M. Yor. Some explicit Krein representations of certain subordinators, including the gamma process. Publ. RIMS, Kyoto, 42(4):879–895, 2006.
5. C. Donati-Martin and M. Yor. Further examples of explicit Krein representations of certain subordinators. Publ. RIMS, Kyoto, 43(4), 2007.
6. D. Dufresne. Algebraic properties of beta and gamma distributions, and applications. Adv. in App. Math., 20(3):285–299, 1998.
7. M. Emery and M. Yor. A parallel between Brownian bridges and gamma bridges. Publ. RIMS, Kyoto Univ., 40(3):669–688, 2004.
8. T. Jeulin and M. Yor. Filtration des ponts Browniens et équations différentielles stochastiques linéaires. Séminaire de Probabilités XXIV, Springer LNM 1426, 227–265, 1990.
9. F. Knight. Characterization of the Lévy measure of inverse local times of gap diffusion. Seminar on Stochastic Processes, eds. E. Cinlar, K. Chung, and R. Getoor, Birkhäuser, 53–78, 1981.
10. S. Kotani and S. Watanabe. Krein’s spectral theory of strings and generalized diffusion process. Functional Analysis in Markov Processes (Katata/Kyoto 1981), Springer LNM 923, 235–259, 1982.
11. D.B. Madan, P. Carr, and E.C. Chang. The variance gamma process and option pricing. European Finance Review, 2:79–105, 1998.
12. D. Madan and E. Seneta. The variance gamma (V.G.) model for share market returns. J. of Business, 63(4):511–524, 1990.
13. R. Mansuy and M.Yor. Harnesses, Lévy bridges and Monsieur Jourdain. Stoch. Proc. and Applications, 115(2):329–338, February 2005.
14. P. Salminen, P. Vallois, and M. Yor. On the excursion theory for linear diffusions. Jap. J. Maths, in honor of K. Itô, 2(1)97–127, 2007.
15. W. Schoutens. Stochastic Processes and Orthogonal Polynomials. LNS 146, Springer, 2000.
16. N. Tsilevich and A. Vershik. Quasi-invariance of the gamma process and multiplicative properties of the Poisson-Dirichlet measures. C. R. Acad. Sci., Paris, Sér. I, 329:163–168, 1999.
17. N. Tsilevich, A. Vershik, and M. Yor. An infinite-dimensional analogue of the Lebesgue measure and distinguished properties of the gamma process. J. Funct. Anal., 185:274–296, 2001.
18. A. Vershik and M. Yor. Multiplicativité du processus gamma et étude asymp-totique des lois stables d’indice α, lorsque α tend vers 0. Prépublication 289, Laboratoire de Probabilités, Paris, 1995.
19. D. Williams. Some basic theorems on harnesses. Stochastic Analysis (A Tribute to the Memory of Rollo Davidson), eds. D. Kendall and H. Harding, Wiley, 1973.
20. M. Yor. Some Aspects of Brownian Motion, Part I: Some Special Functionals. ETH Zürich, Birkhäuser, 1992.
21. M. Yor. On Exponential Functionals of Brownian Motion and Related Processes. Springer, 2001.