Some new examples of Markov processes which enjoy the time-inversion property

Probability Theory and Related Fields

Volumn 132, Issue 1, 2005, Pages 150-162

  Gallardo, Léonard ^a   Yor, Marc ^b  

^a UNIVERSITÉ DE TOURS   (France)

^b SORBONNE UNIVERSITÉ   (France)

Author keywords

"Op rateur carr du champ"; Bessel processes; Dunkl processes; Dunkl processes with drift; Homogeneous Markov processes; Radial Dunkl processes; Semi stable processes; Time inversion property; Wishart processes

Indexed keywords

EID: 17444421579     PISSN: 01788051     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00440-004-0399-y     Document Type: Article

References (24)

1. Biane, P., Bougerol, P., O'Connell, N.: Littlemann paths and Brownian paths. Preprint (March 2004)
2. Bru, M.F.: Processus de Wishart, C.R. Acad. Sci. Paris, Série I, t. 308, 29-32 (1989)
3. Bru, M.F.: Diffusions of perturbed principal component analysis, J. Multivariate Anal. 29, 127-136 (1989)
4. Bru, M.F.: Wishart processes. J. Theor. Prob., 4, 725-751 (1991)
5. Chaumont, L., Yor, M.: Exercises in Probability. A guided Tour from Measure Theory to Random Processes, via Conditioning. Cambridge University Press, 2003
6. Dellacherie, C., Maisonneuve, B., Meyer, P.A.: Probabilités et Potentiels, Chap. XVII à XXIV. Hermann, Paris 1992
7. Donati-Martin, C., Doumerc, Y., Matsumoto, H., Yor, M.: Some properties of the Wishart processes and a matrix extension of the Hartman-Watson laws. To appear in Publ. RIMS, Kyoto, 2004
8. Dunkl, C.: Differential-differences operators associated to reflection groups. Trans. Amer. Math. Soc. 311 (1), 167-183 (1989)
9. Dunkl, C.: Hankel Transforms associated to finite reflection groups. Contemp. Math., 138, 123-138 (1992)
10. Dunkl, C., Xu, Y: Orthogonal Polynomials of Several Variables. Cambridge University Press, 2001
11. Gallardo, L., Yor, M.: Some remarkable properties of the Dunkl martingales, to appear in Sém. Probas. XXXVIII, dedicated to Paul André Meyer. Springer LNM 2005
12. Godefroy, L.: Frontière de Martin sur les hypergroupes et principe d'invariance relatif au processus de Dunkl. Thèse Université de Tours (Déc. 2003)
13. Graversen, S.E., Vuolle-Apiala, J.: On Paul Lévy's arc sine law and Shiga-Watanabe's time-inversion result. Prob. Math. Stat. 20, 63-73 (2000)
14. Hirsch, F.: L'opérateur carré du champ, d'après J.P. Roth. Séminaire Bourbaki, 29 ième année, exposé 501, (juin 1977)
15. Kunita, H.: Absolute continuity of Markov processes and generators. Nagoya Math. J. 36, 1-26 (1969)
16. Lamperti, J.: Semi-stable Markov processes I. Zeit, für Wahr. 22, 205-255 (1972)
17. Pitman, J., Yor, M.: Bessel processes and infinitely divisible laws. In : D. Williams (ed) Stochastic Integrals. Lect. Notes in Math. 851 (1981)
18. Revuz, D., Yor, M.: Continuous Martingales and Brownian Motion. Springer. Third Edition, corrected second printing, 2001
19. Rösler, M.: Generalized Hermite Polynomials and the Heat Equation for Dunkl Operators. Commun. Math. Phys. 192, 519-542 (1998)
20. Rösler, M., Voit, M.: Markov processes related with Dunkl operators. Adv. App. Math. 21 (4), 575-643 (1998)
21. Roth, J.P.: Opérateurs dissipatifs et semi-groupes dans les espaces de fonctions continues. Ann. Inst. Fourier, 26 (4), 1-97 (1976)
22. Watanabe, S.: On time-inversion of one-dimensional diffusion processes. Zeit, für Wahr. 31, 115-124 (1975)
23. Watanabe, S.: Invariants of one-dimensional diffusion processes and applications. In : J. Korean Math. Soc. 35 (3), 659-673 (1998)
24. Watanabe, S.: Bilateral Bessel diffusion processes with drifts and time-inversion. Preprint (1997-1998)