Classification des semi-groupes de diffusion sur associés à une famille de polynômes orthogonaux
Mazet, Olivier
Séminaire de probabilités de Strasbourg, Tome 31 (1997), p. 40-53 / Harvested from Numdam
@article{SPS_1997__31__40_0,
     author = {Mazet, Olivier},
     title = {Classification des semi-groupes de diffusion sur $\mathbb {R}$ associ\'es \`a une famille de polyn\^omes orthogonaux},
     journal = {S\'eminaire de probabilit\'es de Strasbourg},
     volume = {31},
     year = {1997},
     pages = {40-53},
     mrnumber = {1478714},
     zbl = {0883.60072},
     language = {en},
     url = {http://dml.mathdoc.fr/item/SPS_1997__31__40_0}
}
Mazet, Olivier. Classification des semi-groupes de diffusion sur $\mathbb {R}$ associés à une famille de polynômes orthogonaux. Séminaire de probabilités de Strasbourg, Tome 31 (1997) pp. 40-53. http://gdmltest.u-ga.fr/item/SPS_1997__31__40_0/

[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. | MR 1648654 | Zbl 0905.60059

[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. | Numdam | MR 960507 | Zbl 0653.58043

[3] D. Bakry. L'hypercontractivité et son utilisation en théorie des semi-groupes. In Lectures on Probability Theory, volume 1581. Springer-Verlag, 1994. | MR 1307413 | Zbl 0856.47026

[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. | MR 1417973 | Zbl 0859.47026

[5] D. Bakry and M. Emery. Hypercontractivité de semi-groupes de diffusion. C.R.Acad. Paris, 299, Série I(15):775-778, 1984. | MR 772092 | Zbl 0563.60068

[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. | MR 82021 | Zbl 0075.28002

[7] W. Feller. The parabolic differential equations and the associated semi-groups of transformations. Ann. of Math., 55:468-519, 1952. | MR 47886 | Zbl 0047.09303

[8] W. Feller. Diffusion processes in one dimension. Trans. Amer. Math. Soc., 77:1-31, 1954. | MR 63607 | Zbl 0059.11601

[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. | Numdam | MR 215331 | Zbl 0157.24902

[10] G. Gasper. Banach algebras for Jacobi series and positivity of a kernel. Ann. of Math., 2(95):261-280, 1972. | MR 310536 | Zbl 0236.33013

[11] K. Ito and H.P. Mckean. Diffusion processes and their sample paths, volume 125. Springer-Verlag, 1965. | Zbl 0127.09503

[12] S. Karlin and J. Mcgregor. Classical diffusion processes and total positivity. Journal of mathematical analysis and applications, 1:163-183, 1960. | MR 121844 | Zbl 0101.11102

[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. | MR 774055 | Zbl 0584.43010

[14] A. Korzeniowski and D. Stroock. An example in the theory of hypercontractive semigroups. Proc. A.M.S., 94:87-90, 1985. | MR 781062 | Zbl 0577.47043

[15] Pa. Meyer. Note sur le processus d'Ornstein-Uhlenbeck. In Séminaire de probabilités XVI, volume 920, pages 95-133. Springer-Verlag, 1982. | Numdam | MR 658673 | Zbl 0481.60041

[16] O.V. Sarmanov and Z.N. Bratoeva. Probabilistic properties of bilinear expansions of Hermite polynomials. Teor. Verujatnost. i Primenen, 12:470-481, 1967. | MR 216541 | Zbl 0178.21205

[17] T. Shiga and S. Watanabe. Bessel diffusions as a one-parameter family of diffusion processes. Z. Wahrscheinlichkeitstheorie verw. Geb., 27:37-46, 1973. | MR 368192 | Zbl 0327.60047

[18] E.M. Stein and G. Weiss. Introduction to Fourier Analysis on Euclidean Spaces. Princeton University Press, 1971. | MR 304972 | Zbl 0232.42007

[19] D. Stroock. Probability Theory: an analytic view. Cambridge University Press, 1993. | MR 1267569 | Zbl 0925.60004

[20] G. Szegö. Orthogonal Polynomials. American Mathematical Society, 4th edition, 1975. | MR 372517

[21] H.C. Wang. Two-point homogeneous spaces. Annals of Mathematics, 55:177-191, 1952. | MR 47345 | Zbl 0048.40503

[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. | MR 161375 | Zbl 0139.34406

[23] K. Yosida. Functional Analysis. Springer-Verlag, 1968.