Classification des semi-groupes de diffusion sur $ℝ$ associés à une famille de polynômes orthogonaux

 Access to full text

 Full (PDF)

1. [1] L. Alili, D. Dufresne, and M. Yor. Sur l'identité de Bougerol pour les fonctionnelles exponentielles du mouvement Brownien avec drift. A paraître, 1996. Zbl0905.60059MR1648654
2. [2] D. Bakry. La propriété de sous-harmonicité des diffusions dans les variétés. In Séminaire de probabilité XXII, Lectures Notes in Mathematics, volume 1321, pages 1-50. Springer-Verlag, 1988. Zbl0653.58043MR960507
3. [3] D. Bakry. L'hypercontractivité et son utilisation en théorie des semi-groupes. In Lectures on Probability Theory, volume 1581. Springer-Verlag, 1994. Zbl0856.47026MR1307413
4. [4] D. Bakry. Remarques sur les semi-groupes de Jacobi. In Hommage à P.A. Meyer et J. Neveu, volume 236, pages 23-40. Astérisque, 1996. Zbl0859.47026MR1417973
5. [5] D. Bakry and M. Emery. Hypercontractivité de semi-groupes de diffusion. C.R.Acad.Paris, 299, Série I(15):775-778, 1984. Zbl0563.60068MR772092
6. [6] S. Bochner. Sturm-Liouville and heat equations whose eigenfunctions are ultra-spherical polynomials or associated Bessel functions. Proc. Conf. Differential Equations, pages 23-48, 1955. Zbl0075.28002MR82021
7. [7] W. Feller. The parabolic differential equations and the associated semi-groups of transformations. Ann. of Math., 55:468-519, 1952. Zbl0047.09303MR47886
8. [8] W. Feller. Diffusion processes in one dimension. Trans. Amer. Math. Soc., 77:1-31, 1954. Zbl0059.11601MR63607
9. [9] R. Gangolli. Positive definite kernels on homogeneous spaces and certain stochastic processes related to Lévy's Brownian motion of several parameters. Ann. Inst. Henri Poincaré, III(2):9-226, 1967. Zbl0157.24902MR215331
10. [10] G. Gasper. Banach algebras for Jacobi series and positivity of a kernel. Ann. of Math., 2(95):261-280, 1972. Zbl0236.33013MR310536
11. [11] K. Ito and H.P. McKean. Diffusion processes and their sample paths, volume 125. Springer-Verlag, 1965. Zbl0127.09503
12. [12] S. Karlin and J. McGregor. Classical diffusion processes and total positivity. Journal of mathematical analysis and applications, 1:163-183, 1960. Zbl0101.11102MR121844
13. [13] H. Koornwinder. Jacobi functions and analysis on nomcompact semisimple Lie groups. In R.A. Askey et al. (eds.), editor, Special functions: group theoretical aspects and applications, pages 1-85. 1984. Zbl0584.43010MR774055
14. [14] A. Korzeniowski and D. Stroock. An example in the theory of hypercontractive semigroups. Proc. A.M.S., 94:87-90, 1985. Zbl0577.47043MR781062
15. [15] PA. Meyer. Note sur le processus d'Ornstein-Uhlenbeck. In Séminaire de probabilités XVI, volume 920, pages 95-133. Springer-Verlag, 1982. Zbl0481.60041MR658673
16. [16] O.V. Sarmanov and Z.N. Bratoeva. Probabilistic properties of bilinear expansions of Hermite polynomials. Teor. Verujatnost. i Primenen, 12:470-481, 1967. Zbl0178.21205MR216541
17. [17] T. Shiga and S. Watanabe. Bessel diffusions as a one-parameter family of diffusion processes. Z. Wahrscheinlichkeitstheorie verw. Geb., 27:37-46, 1973. Zbl0327.60047MR368192
18. [18] E.M. Stein and G. Weiss. Introduction to Fourier Analysis on Euclidean Spaces. Princeton University Press, 1971. Zbl0232.42007MR304972
19. [19] D. Stroock. Probability Theory: an analytic view. Cambridge University Press, 1993. Zbl0925.60004MR1267569
20. [20] G. Szegö. Orthogonal Polynomials. American Mathematical Society, 4th edition, 1975. Zbl0305.42011MR372517
21. [21] H.C. Wang. Two-point homogeneous spaces. Annals of Mathematics, 55:177-191, 1952. Zbl0048.40503MR47345
22. [22] E. Wong. The construction of a class of stationary Markov processes. Amer. Math. Soc., Proc. of the XVIth Symp. of App. Math., pages 264-276, 1964. Zbl0139.34406MR161375
23. [23] K. Yosida. Functional Analysis. Springer-Verlag, 1968. Zbl0152.32102

1. Jonathan Warren, Marc Yor, The brownian burglar : conditioning brownian motion by its local time process
2. Abdellatif Bentaleb, Sur les fonctions extrémales des inégalités de Sobolev des opérateurs de diffusion
3. Michel Ledoux, The geometry of Markov diffusion generators