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Uniform and nonuniform proximity bounds for the distributions of two normalized sums of independent random variables with values in Banach spaces

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Literature Cited

  1. V. Bernotas, “Proximity of the distributions of two sums of independent random variables with values in certain Banach spaces,” Litov. Mat. Sb.,18, No. 4, 5–12 (1978).

    Google Scholar 

  2. V. Bernotas and V. I. Paulauskas, “A nonuniform bound in the central limit theorem in certain Banach spaces,” Litov. Mat. Sb.,19, No. 2, 23–43 (1979).

    Google Scholar 

  3. V. M. Zolotarev, “Metric distances in spaces of random variables and their distributions,” Mat. Sb.,101, (143), No. 3, 104–141 (1976).

    Google Scholar 

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

    Google Scholar 

  5. A. Cartan, Differential Calculus. Differential Forms, Houghton Mifflin Co., New York (1970).

    Google Scholar 

  6. V. V. Kvaratskheliya, “Probability distributions in certain spaces of sequences,” Author's Abstract of Candidate's Dissertation, Kiev (1977).

  7. V. I. Paulauskas, “Rate of convergence of certain functionals of sums of independent random variables in a Banach space,” Litov. Mat. Sb.,16, No. 3, 103–121 (1976).

    Google Scholar 

  8. V. I. Paulauskas, “A nonuniform bound in the central limit theorem in a Hilbert space,” Litov. Mat. Sb.,15, No. 4, 177–190 (1975).

    Google Scholar 

  9. V. I. Paulauskas, “Rate of convergence in the central limit theorem in certain Banach spaces,” Teor. Veroyatn. Ee Primen.,21, No. 4, 775–791 (1976).

    Google Scholar 

  10. V. I. Paulauskas, “Limit, theorems for sums of independent random variables with values in finite-dimensional and infinite-dimensional Banach spaces,” Doctoral Dissertation, Vilnius (1978).

  11. J. Hoffman-Jorgenson and G. Pisier, “The law of large numbers and the central limit theorem in Banach spaces,” Ann. Prob.,4, No. 4, 587–599 (1976).

    Google Scholar 

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V. Kapsukas Vilnius State University. Translated from Litovskii Matematicheskii Sbornik (Lietuvos Matematikos Rinkinys), Vol. 19, No. 4, pp. 55–68, October–December, 1979.

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Bernotas, V. Uniform and nonuniform proximity bounds for the distributions of two normalized sums of independent random variables with values in Banach spaces. Lith Math J 19, 482–490 (1979). https://doi.org/10.1007/BF00970719

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