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Mehler-Type Semigroups on Hilbert Spaces and Their Generators

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Stochastic Analysis and Mathematical Physics

Part of the book series: Progress in Probability ((PRPR,volume 50))

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Abstract

In this paper, we shall give a survey of recent work ([1], [3], [5], [6]) on generalized Mehler semigroups by Michaël Röckner and his collaborators.1

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References

  1. V. Bogachev and M. Röckner, Mehler formula and capacities for infinite dimensional Ornstein-Uhlenbeck processes with general linear drift, Osaka J. Math., 32 (1995), 237–274.

    MathSciNet  MATH  Google Scholar 

  2. V. Bogachev, P. Lescot, and M. Röckner, The martingale problem for pseudo-differential operators on infinite-dimensional spaces, Nagoya Mathematical Journal, 153 (1999), 101–118.

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  3. V. Bogachev, M. Röckner, and B. Schmuland Generalized Mehler semigroups and applications, Probability Theory and Related Fields, 105 (1996), 193–225.

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  4. Ph. Courrège, Sur la forme intégro-différentielle du générateur infinitésimal d’un semi-groupe de Feller sur une variété, Séminaire de Théorie du Potentiel (1965-1966), 48pp.

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  5. M. Fuhrman and M. Röckner, Generalized Mehler semigroups-the non-Gaussian case, Potential Analysis, 12 (2000), 1–47.

    Article  MathSciNet  MATH  Google Scholar 

  6. P. Lescot and M. Röckner, Generators of Mehler-type semigroups as pseu-dodifferential operators, preprint Bielefeld, 2000; to appear in Infinite Dimensional Analysis and Quantum Probability.

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  7. W. Linde, Probability in Banach Spaces-Stable and Infinitely Divisible Distributions, John Wiley and Sons, 1986.

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  8. F.G. Mehler, Ueber die Entwicklung einer Function von beliebig vielen Vari-ablen nach Laplaceschen Functionen höheren Ordnung, Journal de Crelle, 66(2), (1866), 161–176.

    Article  MathSciNet  MATH  Google Scholar 

  9. A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer-Verlag, 1983.

    Book  MATH  Google Scholar 

  10. I.E. Segal, Tensor algebras over Hilbert spaces-I, Trans. Amer. Math. Soc., 81(1956), 106–134.

    Article  MATH  Google Scholar 

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Lescot, P. (2001). Mehler-Type Semigroups on Hilbert Spaces and Their Generators. In: Cruzeiro, A.B., Zambrini, JC. (eds) Stochastic Analysis and Mathematical Physics. Progress in Probability, vol 50. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-0127-4_5

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  • DOI: https://doi.org/10.1007/978-1-4612-0127-4_5

  • Publisher Name: Birkhäuser, Boston, MA

  • Print ISBN: 978-1-4612-6624-2

  • Online ISBN: 978-1-4612-0127-4

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