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A new method to prove Strassen type laws of invariance principle. I. (English) Zbl 0283.60023

MSC:
60F15 Strong limit theorems
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[1] Strassen, V.: Almost sure behaviour of sums of independent random variables and martingales. Proc. 5th Berkeley Sympos. Math. Statist. Probab. (1965), Vol. II (part 1), 315–343. Berkeley: Univ. of Calif. Press 1967
[2] Kiefer, J.: On the deviations in the Skorohod-Strassen approximation scheme. Z. Wahrscheinlichkeitstheorie verw. Gebiete 13, 321–332 (1969) · Zbl 0176.48201 · doi:10.1007/BF00539208
[3] Cramér, H.: Random variables and probability distributions. 2nd ed. Cambridge: Cambridge Univ. Press 1962 · Zbl 0105.24406
[4] Gnedenko, B. V., Kolmogorov, A. N.: Limit distributions for sums of independent random variables. Cambridge: Addison-Wesley 1954 · Zbl 0056.36001
[5] Rubin, H., Sethuraman, J.: Probabilities of moderate deviations. Sankhya Ser. A., 27, 325–346 (1965) · Zbl 0178.53802
[6] Breiman, L.: On the tail behaviour of sums of independent random variables. Z. Wahrscheinlichkeitstheorie verw. Gebiete 9, 20–25 (1967) · Zbl 0339.60050 · doi:10.1007/BF00535464
[7] Borovkov, A.A.: On the speed of convergence in the invariance principle (in Russ). Teor. Verojatnost. i Primenen. 18, 217–234 (1973)
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