Literature Cited
F. Spitzer, “A combinatorial lemma and its application to probability theory,” Trans. Amer. Math. Soc.,82, 323–339 (1956).
A. A. Borovkov, “New limit theorems in boundary value problems for the sums of independent terms,” Sibirsk. Matem. Zh.,3, No. 5, 645–694 (1962).
A. A. Borovkov and V. S. Korolyuk, “On the results of asymptotic analysis in problems with boundaries,” Teoriya Veroyatn. i Eyo Primen.,10, No. 2, 255–266 (1965).
V. V. Petrov, “On local limit theorems for sums of independent random quantities,” Teoriya Veroyatn. i Eyo Primen.,9, No. 2, 343–351 (1964).
L. V. Osipov, “Asymptotic expansions in the central limit theorem,” Vestnik Leningrad Gos. Univ., No. 19, 45–62 (1967).
S. V. Nagaev, “Estimating the convergence rate of the distribution of the maximum of sums of independent random quantities,” Sibirsk. Matem. Zh.,10, No. 3, 614–633 (1969).
S. V. Nagaev, “On the convergence rate of the distribution of the maximum of sums of independent random quantities,” Teoriya Veroyatn. i Eyo Primen.,15, No. 2 (1970).
S. V. Negaev, “On the convergence rate in a certain boudary value problem,” Teoriya Veroyatn. i Eyo Primen.,15, No. 2 (1970).
B. V. Gnedenko and A. N. Kolmogorov, Limit Distributions for Sums of Independent Random Quantities [in Russian], Mosow-Leningrad (1949).
A. O. Gel'fond, Calculus of Finite Differences [in Russian], Moscow (1959).
J. Riordan, Introduction to Combinatorial Analysis [Russian translation], Moscow (1963).
V. S. Korolyuk, Asymptotic Analysis in Boundary Value Problems Involving Random Walks, Dissertation [in Russian], Mathematics Institute, Kiev (1963).
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Translated from Sibirskii Matematicheskii Zhurnal, Vol. 11, No. 2, pp. 381–406, March–April, 1970.
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Nagaev, S.V. Asymptotic expansions for the distribution function of the maximum of a sum of independent identically distributed random quantities. Sib Math J 11, 288–309 (1970). https://doi.org/10.1007/BF00967303
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DOI: https://doi.org/10.1007/BF00967303