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Convergence to Stable Laws in Relative Entropy

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Convergence to stable laws in relative entropy is established for sums of i.i.d. random variables.

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References

  1. Barron, A.R.: Entropy and the central limit theorem. Ann. Probab. 14(1), 336–342 (1986)

    Article  MathSciNet  MATH  Google Scholar 

  2. Bobkov, S.G., Chistyakov, G.P., Götze, F.: Rate of convergence and Edgeworth-type expansion in the entropic central limit theorem. Preprint (2011). Bielefeld University, Bielefeld. arXiv:1104.3994v1 [math.PR], 20 April 2011

  3. Ibragimov, I.A., Linnik, Ju.V.: Independent Stationarily Connected Variables. Nauka, Moscow (1965). 524 pp

    MATH  Google Scholar 

  4. Johnson, O.: Information Theory and the Central Limit Theorem. Imperial College Press, London (2004), xiv+209 pp

    Book  MATH  Google Scholar 

  5. Lamperti, J.W.: Probability. A Survey of the Mathematical Theory, 2nd edn. Wiley Series in Probability and Statistics: Probability and Statistics. Wiley, New York (1996) xii+189 pp

    Book  MATH  Google Scholar 

  6. Linnik, Yu.V.: An information-theoretic proof of the central limit theorem with the Lindeberg condition. Theory Probab. Appl. 4, 288–299 (1959)

    Article  MathSciNet  Google Scholar 

  7. Petrov, V.V.: Sums of Independent Random Variables. Springer, New York (1975) x + 345 pp

    Book  Google Scholar 

  8. Zolotarev, V.M.: One-dimensional Stable Distributions. Probability Theory and Mathematical Statistics. Nauka, Moscow (1983) 304 pp

    MATH  Google Scholar 

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Correspondence to F. Götze.

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Bobkov, S.G., Chistyakov, G.P. & Götze, F. Convergence to Stable Laws in Relative Entropy. J Theor Probab 26, 803–818 (2013). https://doi.org/10.1007/s10959-011-0377-0

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  • DOI: https://doi.org/10.1007/s10959-011-0377-0

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