An approximation of partial sums of independent RV’s, and the sample DF. I. (English) Zbl 0308.60029


60G50 Sums of independent random variables; random walks
62D05 Sampling theory, sample surveys
Full Text: DOI


[1] Bártfai, P., Die Bestimmung der zu einem wiederkehrenden Prozegehörenden Verteilungsfunktion aus den mit Fehlern behafteten Daten einer einzigen Realisation, Studia Sci. Math. Hungar., 1, 161-168 (1966) · Zbl 0156.39102
[2] Bártfai, P., über die Entfernung der Irrfahrtswege, Studia Sci. Math. Hungar., 5, 41-49 (1970) · Zbl 0274.60048
[3] Breiman, L., Probability (1968), Reading, Mass: Addison-Wesley, Reading, Mass · Zbl 0174.48801
[4] Brillinger, D. R., An asymptotic representation of the sample df, Bull. Amer. Math. Soc., 75, 545-547 (1969) · Zbl 0206.20602
[5] CsörgŐ, M.; Révész, P., A new method to prove Strassen type laws of Invariance Principle I.-II, Z. Wahrscheinlichkeitstheorie verw. Geb., 31, 255-259 (1975) · Zbl 0283.60023
[6] ErdŐs, P.; Rényi, A., On a new law of large numbers, J. Analyse Math., 23, 103-111 (1970) · Zbl 0225.60015
[7] Kiefer, J., On the deviations in the Skorohod-Strassen approximation scheme, Z. Wahrscheinlichkeitstheorie verw. Geb., 13, 321-332 (1969) · Zbl 0176.48201
[8] Kiefer, J., Skorohod embedding of multivariate RV’s, and the sample DF, Z. Wahrscheinlichkeitstheorie verw. Geb., 24, 1-35 (1972) · Zbl 0267.60034
[9] Petrov, V. V., On large deviations of sums of random variables, Vestnik Leningrad. Univ., 16, 25-37 (1961) · Zbl 0118.13601
[10] Petrov, V. V., On sums of independent random variables (1972), Moscow: Nauka, Moscow · Zbl 0288.60050
[11] Richter, W., Local limit theorems for large deviations (Russian) Teor, Verojatnost. i Primenen, 2, 214-229 (1957) · Zbl 0080.34302
[12] Sawyer, S., Rates of convergence for some functionals in probability, Ann. Math. Statist., 43, 273-284 (1972) · Zbl 0239.60024
[13] Skorohod, A. V., Studies in the theory of random processes (1965), Reading, Mass: Addison-Wesley, Reading, Mass · Zbl 0146.37701
[14] Strassen, V., Almost sure behaviour of sums of independent random variables and martingales, Proc. 5th Berkeley Sympos. Math. Statist. Probab. (1965), Vol. II, 315-343 (1967), Berkeley: Univ. of Calif. Press, Berkeley · Zbl 0201.49903
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.