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Berk, K.N.: A central limit theorem for m-dependent random variables with unbounded m. Ann. Probab. 1, 352–354 (1973)
Erickson, R.V.: L 1 bounds for asymptotic normality of m-dependent sums using Stein's technique. Ann. Probab. 2, 522–529 (1974)
Heinrich, L.: On a factorization of the characteristic function of a sum of dependent random variables (German). Liet. mat. rink. 22, 190–202 (1982)
Heinrich, L.: On probabilities of large deviations for sums of random variables connected in a Markov chain under a non-Cramérian type condition (German). Liet. mat. rink. (To appear)
Heinrich, L.: A new approach to the summation theory of random variables connected in a Markov chain. Math. Nachr. (To appear, 1982)
Heinrich, L.: Infinitely divisible distributions as limit laws for sums of random variables connected in a Markov chain. Math. Nachr. (To appear, 1982)
Petrov, V.V.: On the central limit theorem for m-dependent random variables (Russian). In: Proc. All-Union-Conf. Prob. Theory and Math. Statistics, Erevan 1958, pp. 138–144. Erevan: Izdat. Akad. Nauk Armjan. SSR 1960
Petrov, V.V.: Sums of independent random variables. Berlin-Heidelberg-New York: Springer 1975
Shergin, V.V.: On the speed of convergence in the central limit theorem for m-dependent random variables (Russian). Teor. verojatn. primen. 24, 781–794 (1979)
Statulevičius, V.A.: On large deviations. Z. Wahrscheinlichkeitstheorie verw. Gebiete 6, 133–144 (1966)
Statulevičius, V.A.: On limit theorems for random functions I (Russian). Liet. mat. rink. 10, 583–592 (1970)
Stein, C.: A bound for the error in the normal approximation to the distribution of a sum of dependent random variables. In: Proc. 6th Berkeley Sympos. Math. Statistics Probab., Vol. 2, pp. 583–602. Berkeley: Univ. Calif. Press 1972
Tichomirov, A.N.: On the speed of convergence in the central limit theorem for weakly dependent random variables (Russian). Teor. verojatn. primen. 25, 800–818 (1980)
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Heinrich, L. A method for the derivation of limit theorems for sums of m-dependent random variables. Z. Wahrscheinlichkeitstheorie verw Gebiete 60, 501–515 (1982). https://doi.org/10.1007/BF00535713
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DOI: https://doi.org/10.1007/BF00535713