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Asymptotic expansions for large deviations when Cramer's condition fails

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Literature cited

  1. I. A. Ibragimov and Yu. V. Linnik, Independent and Stationary Related Variables [in Russian], Moscow (1965).

  2. Yu. V. Linnik, “New limit theorems for the sums of independent random variables,” Dokl. Akad. Nauk SSSR,133, No. 6, 1291–1293 (1960).

    Google Scholar 

  3. Yu. V. Linnik, “Limit theorems for sums of independent variables taking account of large deviations I–III,” Teor. Veroyatn. i Ee Primen.,6, 145–163, 377–391 (1961);7, 121–134 (1962).

    Google Scholar 

  4. V. Rikhter, “Local limit theorems for large deviations,” Teor. Veroyatn. i Ee Primen.,2, No. 2, 214–229 (1957).

    Google Scholar 

  5. V. Rikhter, “A local limit theorem for large deviations,” Dokl. Akad. Nauk SSSR,115, No. 1, 53–56 (1957).

    Google Scholar 

  6. V. V. Petrov, “Large deviations of sums of random variables,” Vestnik LGU, No. 1, 23–27 (1961).

    Google Scholar 

  7. V. V. Petrov, “The extension of Cramer's limit theorem to nonidentical distributions of independent variables,” Vestnik LGU, No. 8, 13–25 (1963).

    Google Scholar 

  8. V. V. Petrov, “Limit theorems for large deviations when Cramer's condition fails, Vols, 1 and 2 Vestnik LGU, No. 19, 49–68 (1963); No. 1, 52–75 (1964).

    Google Scholar 

  9. V. V. Petrov, “The asymptotic behavior of the probabilities of large deviations,” Teor. Veroyatn. i Ee Primen.,13, No. 2, 432–444 (1968).

    Google Scholar 

  10. V. A. Statulevičius, “On large deviations,” Zeitschrift für Wahrscheinlichkeitstheorie und verwandte Gebeite, Band 6, Heft 2, 133–144 (1966).

    Google Scholar 

  11. V. Vol'f, “Certain limit theorems for large deviations,” Dokl. Akad. Nauk SSSR,178, No. 1, 21–23 (1968).

    Google Scholar 

  12. V. Vol'f, “Certain limit theorems for large deviations of sums of independent random variables,” Candidate's Dissertation [in Russian], Leningrad (1968).

  13. I. I. Privalov, Introduction to the Theory of Functions of a Complex Variable [in Russian], Moscow (1960).

  14. E. Misevichyus and L. Saulis, “Expansions of local large deviations,” Litovsk. Matem. Sb.,13, 000 (1973).

    Google Scholar 

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Deceased.

Translated from Litovskii Matematicheskii Sbornik, Vol. 13, No. 1, pp. 199–219, January–March, 1973.

The authors wish to thank V. Statulevičius for formulating the problem. They are grateful to E. Misevichyus for useful discussions.

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Saulis, L., Nakas, A. Asymptotic expansions for large deviations when Cramer's condition fails. Lith Math J 13, 141–155 (1973). https://doi.org/10.1007/BF01540085

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