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Classification des Semi-Groupes de diffusion sur IR associés à une famille de polynômes orthogonaux

Part of the Lecture Notes in Mathematics book series (SEMPROBAB,volume 1655)

Keywords

  • Generateur Infinitesimal
  • Positive Definite Kernel
  • Mouvement Brownien
  • Selon Laquelle
  • Hypercontractive Semigroup

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References

  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.

    Google Scholar 

  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.

    Google Scholar 

  3. D. Bakry. L’hypercontractivité et son utilisation en théorie des semi-groupes. In Lectures on Probability Theory, volume 1581. Springer-Verlag, 1994.

    Google Scholar 

  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.

    Google Scholar 

  5. D. Bakry and M. Emery. Hypercontractivité de semi-groupes de diffusion. C.R.Acad. Paris, 299, Série I (15):775–778, 1984.

    MathSciNet  MATH  Google Scholar 

  6. S. Bochner. Sturm-Liouville and heat equations whose eigenfunctions are ultraspherical polynomials or associated Bessel functions. Proc. Conf. Differential Equations, pages 23–48, 1955.

    Google Scholar 

  7. W. Feller. The parabolic differential equations and the associated semi-groups of transformations. Ann. of Math., 55:468–519. 1952.

    CrossRef  MathSciNet  MATH  Google Scholar 

  8. W. Feller. Diffusion processes in one dimension. Trans. Amer. Math. Soc., 77:1–31, 1954.

    CrossRef  MathSciNet  MATH  Google Scholar 

  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.

    MATH  Google Scholar 

  10. G. Gasper. Banach algebras for Jacobi series and positivity of a kernel. Ann. of Math., 2(95):261–280, 1972.

    CrossRef  MathSciNet  MATH  Google Scholar 

  11. K. Ito and H. P. McKean. Diffusion processes and their sample paths, volume 125. Springer-Verlag, 1965.

    Google Scholar 

  12. S. Karlin and J. McGregor. Classical diffusion processes and total positivity. Journal of mathematical analysis and applications, 1:163–183, 1960.

    CrossRef  MathSciNet  MATH  Google Scholar 

  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.

    Google Scholar 

  14. A. Korzeniowski and D. Stroock. An example in the theory of hypercontractive semigroups. Proc. A.M.S., 94:87–90, 1985.

    CrossRef  MathSciNet  MATH  Google Scholar 

  15. PA. Meyer. Note sur le processus d’Ornstein-Uhlenbeck. In Séminaire de probabilités XVI, volume 920, pages 95–133. Springer-Verlag, 1982.

    Google Scholar 

  16. O.V. Sarmanov and Z.N. Bratoeva. Probabilistic properties of bilinear expansions of Hermite polynomials. Teor. Verujatnost. i Primenen, 12:470–481, 1967.

    MathSciNet  MATH  Google Scholar 

  17. T. Shiga and S. Watanabe. Bessel diffusions as a one-parameter family of diffusion processes. Z. Wahrscheinlichkeitstheorie verw. Geb., 27:37–46, 1973.

    CrossRef  MathSciNet  MATH  Google Scholar 

  18. E.M. Stein and G. Weiss. Introduction to Fourier Analysis on Euclidean Spaces. Princeton University Press, 1971.

    Google Scholar 

  19. D. Stroock. Probability Theory: an analytic view. Cambridge University Press, 1993.

    Google Scholar 

  20. G. Szegö. Orthogonal Polynomials. American Mathematical Society, 4th edition, 1975.

    Google Scholar 

  21. H.C. Wang. Two-point homogeneous spaces. Annals of Mathematics, 55:177–191, 1952.

    CrossRef  MathSciNet  MATH  Google Scholar 

  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.

    Google Scholar 

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

    Google Scholar 

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Mazet, O. (1997). Classification des Semi-Groupes de diffusion sur IR associés à une famille de polynômes orthogonaux. In: Azéma, J., Yor, M., Emery, M. (eds) Séminaire de Probabilités XXXI. Lecture Notes in Mathematics, vol 1655. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0119290

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  • DOI: https://doi.org/10.1007/BFb0119290

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