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Conditions for the smoothness of the density of the distribution of the Lp -norm of a Gaussian vector

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Abstract

In this paper sufficient conditions are given for the smoothness indicated in the title. The restrictions on the Gaussian measure are connected only with the dimension of its topological support.

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Literature cited

  1. N. V. Smorodina, “Smoothness conditions for densities of distributions of functionals of stochastic processes,” in: Abstracts of Reports to the Fourth International Vilnius Conference on Probability Theory and Mathematical Statistics [in Russian], Vol. 3, Vilnius (1985), pp. 143–145.

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  2. T. R. Vinogradova, “Estimates of rate of convergence in limit theorems,” Author's Abstrate of Candidate's Dissertation, Moscow (1985).

  3. A. V. Uglanov, “Integration on Banach manifolds and its application to the theory of stochastic processes,” in: Abstracts of Reports to the First Whole-World Congress of the Bernouli Mathematical Statistics and Probability Theory Society [in Russian], Vol. 2, Tashkent (1986), p. 878.

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  4. Kh.-S. Go, Gaussian Measures in Banach Spaces [Russian translation], Mir, Moscow (1979).

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  5. N. N. Vakhaniya, V. I. Tarieladze, and S. A. Chobanyan, Probabilistic Distributions in Banach Spaces [in Russian], Nauka, Moscow (1985).

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  6. N. V. Smorodina, “Differential calculus on measure spaces and smoothness conditions for densities of distributions of random variables,” Dokl. Akad. Nauk SSSR (1986).

  7. N. Ikeda and S. Watanabe, Stochastic Differential Equations and Diffusion Processes, North-Holland/Kodansha (1981).

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Authors
  1. N. V. Smorodina
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Additional information

Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 158, pp. 161–166, 1987.

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Smorodina, N.V. Conditions for the smoothness of the density of the distribution of the Lp -norm of a Gaussian vector. J Math Sci 43, 2849–2853 (1988). https://doi.org/10.1007/BF01129903

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  • DOI: https://doi.org/10.1007/BF01129903

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