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Approximation by distributions of sums of smoothly dependent random variables

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Literature Cited

  1. V. M. Zolotarev, “Approximation of distributions of sums of independent random variables with values in infinite-dimensional spaces,” Teor. Veroyatn. Primen.,21, No. 4, 741–758 (1976).

    Google Scholar 

  2. V. M. Zolotarev, “Ideal metrics in the problem of approximation of distributions of sums of random variables,” Teor. Veroyatn. Primen.,22, No. 3, 449–465 (1977).

    Google Scholar 

  3. V. Bentkus and A. Rachkauskas, “Bounds on the rate of convergence in the central limit theorem in the Prokhorov metric,” Dokl. Akad. Nauk SSSR,264, No. 3, 521–524 (1982).

    Google Scholar 

  4. P. P. Gudinas, “Approximation of distributions of sums of dependent random variables with values in a Banach space,” Liet. Mat. Rinkinys,23, No. 3, 3–21 (1983).

    Google Scholar 

  5. P. P. Gudinas, “Approximation by distributions of sums of conditionally independent random variables,” Liet. Mat. Rinkinys,24, No. 4, 60–67 (1984).

    Google Scholar 

  6. V. V. Senatov, “Uniform bounds on the rate of convergence in the multidimensional central limit theorem,” Teor. Veroyatn. Primen.,25, No. 4, 757–770 (1980).

    Google Scholar 

  7. I. I. Gikhman and A. V. Skorokhod, Theory of Stochastic Processes [in Russian], Nauka, Moscow (1971).

    Google Scholar 

  8. J. Neveu, Mathematical Foundations of Probability Theory [Russian translation], Mir, Moscow (1969).

    Google Scholar 

  9. H. Cartan, Differential Calculus, Differential Forms [Russian translation], Mir, Moscow (1971).

    Google Scholar 

  10. E. Bolthausen, “Exact convergence rates in some martingale central limit theorems,” Ann. Probab.,10, No. 3, 672–688 (1982).

    Google Scholar 

  11. V. V. Sazonov, “On a bound for the rate of convergence in the multidimensional central limit theorem,” in: Proc. Sixth Berkeley Symp. Math. Statist. Probab., Vol. 2 (1972). pp. 563–581.

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Authors
  1. P. Gudynas
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Institute of Mathematics and Cybernetics, Academy of Sciences of the Lithuanian SSR. Translated from Litovskii Matematicheskii Sbornik (Lietuvos Matematikos Rinkinys), Vol. 25, No. 4, pp. 53–71, October–December, 1985.

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Gudynas, P. Approximation by distributions of sums of smoothly dependent random variables. Lith Math J 25, 330–343 (1985). https://doi.org/10.1007/BF00968330

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  • DOI: https://doi.org/10.1007/BF00968330

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