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References
Billingsley, P.: Convergence of probability measures. New York: Wiley 1968
Bingham, N.H.: On Valiron and circle convergence. Math. Z.186, 273–286 (1984)
Bingham, N.H., Maejima, M.: Summability methods and almost sure convergence. Z. Wahrscheinlichkeitstheor. Verw. Geb.68, 383–392 (1985)
Chow, Y.S.: Delayed sums and Borel summability of independent identically distributed random variables. Bull. Inst. Math. Acad. Sinica1, 207–220 (1973)
Durrett, R., Resnick, S.I.: functional limit theorems for dependent random variables. Ann. Probab.6, 829–846 (1978)
Embrechts, P., Maejima, M.: The central limit theorem for summability methods of i.i.d. random variables. Z. Wahrscheinlichkeitstheor. Verw. Geb.68, 191–204 (1984)
Hardy, G.H.: Divergent series. Oxford: University Press 1967
Holley, R., Stroock, D.W.: Central limit phenomena of various interacting systems. Ann. Math.110, 333–393 (1979)
Kasahara, Y., Watanabe, S.: Limit theorems for point processes and their functionals. To appear in J. Math. Soc. Japan
Lai, T.L.: Summability methods for independent identically distributed random variables. Proc. Am. Math. Soc.45, 253–261 (1974)
Lindvall, T.: Weak convergence of probability measures and random functions in the function spaceD[0,∞). J. Appl. Probab.10, 109–121 (1973)
Omey, E.: A limit theorem for discounted sums. Z. Wahrscheinlichkeitstheor. Verw. Geb.68, 49–51 (1984)
Petrov, V.V.: Sums of independent random variables. Berlin-Heidelberg-New York: Springer 1975
Pólya, G., Szegö, G.: Problems and theorems in analysis, I. Berlin-Heidelberg-New York: Springer 1972
Shukri, E.M.: Local limit theorems for sums of weighted independent random variables. Theory Probab. Appl.21, 137–144 (1976)
Skorohod, A.V.: Limit theorems for stochastic processes with independent increments. Theory Probab. Appl.2, 138–171 (1957)
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Kasahara, Y., Maejima, M. Functional limit theorems for weighted sums of I.I.D. random variables. Probab. Th. Rel. Fields 72, 161–183 (1986). https://doi.org/10.1007/BF00699101
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DOI: https://doi.org/10.1007/BF00699101