An almost sure limit theorem for moving averages of random variables between the strong law of large numbers and the Erdös-Rényi law
ESAIM: Probability and Statistics, Tome 2 (1998), pp. 163-183. 
@article{PS_1998__2__163_0,
     author = {Lanzinger, Hartmut},
     title = {An almost sure limit theorem for moving averages of random variables between the strong law of large numbers and the {Erd\"os-R\'enyi} law},
     journal = {ESAIM: Probability and Statistics},
     pages = {163--183},
     publisher = {EDP-Sciences},
     volume = {2},
     year = {1998},
     mrnumber = {1655989},
     zbl = {0915.60049},
     language = {en},
     url = {http://www.numdam.org/item/PS_1998__2__163_0/}
}
TY  - JOUR
AU  - Lanzinger, Hartmut
TI  - An almost sure limit theorem for moving averages of random variables between the strong law of large numbers and the Erdös-Rényi law
JO  - ESAIM: Probability and Statistics
PY  - 1998
SP  - 163
EP  - 183
VL  - 2
PB  - EDP-Sciences
UR  - http://www.numdam.org/item/PS_1998__2__163_0/
LA  - en
ID  - PS_1998__2__163_0
ER  - 
%0 Journal Article
%A Lanzinger, Hartmut
%T An almost sure limit theorem for moving averages of random variables between the strong law of large numbers and the Erdös-Rényi law
%J ESAIM: Probability and Statistics
%D 1998
%P 163-183
%V 2
%I EDP-Sciences
%U http://www.numdam.org/item/PS_1998__2__163_0/
%G en
%F PS_1998__2__163_0
Lanzinger, Hartmut. An almost sure limit theorem for moving averages of random variables between the strong law of large numbers and the Erdös-Rényi law. ESAIM: Probability and Statistics, Tome 2 (1998), pp. 163-183. http://www.numdam.org/item/PS_1998__2__163_0/

De Acosta, A. and Kuelbs, J. ( 1983). Limit theorems for moving averages of independent random vectors. Z. Wahrscheinlichkeitstheorie verw. Geb. 64, 67-123. | MR | Zbl

Bingham, N.H. ( 1985). On Tauberian theorems in probability theory. Nieuw. Arch. Wisk. (4) 3. 2 143-149. | MR | Zbl

Bingham, N.H. ( 1988). Moving averages, in: Almost everywhere convergence I. Academic Press. 131-145. | MR | Zbl

Bingham, N.H. and Goldie, C.M. ( 1983). On one-sided Tauberian conditions. Analysis. 3, 159-188. | MR | Zbl

Bingham, N.H. and Goldie, C.M. ( 1983). Riesz means and self-neglecting functions. Math. Z. 199, 443-454. | MR | Zbl

Bingham, N.H. and Maejima, M. ( 1985). Summability methods and almost sure convergence. Z. Wahrscheinlichkeitstheorie verw. Geb. 68, 383-392. | MR | Zbl

Bingham, N.H. and Stadtmüller, U. ( 1990). Jakimovski methods and almost sure convergence, in: Disorder in Physical Systems. Grimmett, Welsh Eds.; Clarendon Press, Oxford. 5-17. | MR | Zbl

Bingham, N.H. and Tenenbaum, G.( 1986). Riesz and Valiron means and fractional moments. Math. Proc. Cambridge Philos. Soc. 99, 143-149. | MR | Zbl

Bingham, N.H., Goldie, C.M. and Teugels, J.L. ( 1987). Regular variation. Cambridge University Press. | MR | Zbl

Chow, Y.S. ( 1973). Delayed sums and Borel summability of independent, identically distributed random variables. Bull. Inst. Math. Acad. Sinica. 1, 207-220. | MR | Zbl

Csörgö, M. and Steinebach, J. ( 1981). Improved Erdös-Rényi and strong approximation laws for increments of partial sums. Ann. Probab. 9, 988-996. | MR | Zbl

Deheuvels, P. and Devroye, L. ( 1987). Limit laws of Erdös-Rényi-Shepp type. Ann. Probab. 15, 1363-1386. | MR | Zbl

Erdös, P. and Rényi, A. ( 1970). On a new law of large numbers. J. Anal. Math. 23, 103-111. | MR | Zbl

Feller, W. ( 1968). An extension of the law of the iterated logarithm to variables without variance. J. Math. Mech. 18, 343-355. | MR | Zbl

Gantert, N. ( 1996). Large deviations for a heavy-tailed mixing sequence. Preprint.

Griffin, P.S. ( 1988). The influence of extremes on the law of the iterated logarithm. Probab. Theory Related Fields. 77, 241-270. | MR | Zbl

Griffin, P.S. ( 1988a). Non-classical law of the iterated logarithm behaviour for trimmed sums. Probab. Theory Related Fields. 78, 293-319. | MR | Zbl

Kiesel, R. ( 1993). General Nörlund Transforms and Power series Methods. Math. Z. 214, 273-286. | EuDML | MR | Zbl

Kiesel, R. ( 1993a). Power series methods and almost sure covergence. Math. Proc. Cambridge Philos. Soc. 113, 195-205. | MR | Zbl

Kiesel, R. and Stadtmüller, U. ( 1996). Erdös-Rényi-Shepp-Laws and weighted sums of i.i.d. random variables. J. Theoret. Probab. 6, 961-982. | MR | Zbl

Kolmogoroff, A.N. ( 1930). Sur la loi forte des grands nombres. C. R. Acad. Sci. Paris. 191, 910-912. | JFM

Kolmogoroff, A.N. ( 1933). Grundbegriffe der Wahrscheinlichkeitsrechnung. Springer Verlag. | JFM | MR | Zbl

Komlós, J., Major, P. and Tusnády, G. ( 1975). An approximation of partial sums of independent rv's and the sample df. I. Z. Wahrscheinlichkeitstheorie verw. Geb. 32, 111-131. | MR | Zbl

Komlós, J., Major, P. and Tusnády, G. ( 1976). An approximation of partial sums of independent rv's and the sample df. II. Z. Wahrscheinlichkeitstheorie verw. Geb. 34, 33-58. | MR | Zbl

Lai, T.L. ( 1974). Summability methods for independent, identically distributed random variables. Proc. Amer. Math. Soc. 45, 253-261. | MR | Zbl

Lai, T.L. ( 1974a). Limit theorems for delayed sums. Ann. Probab. 2, 432-440. | MR | Zbl

Major, P. ( 1976). The approximation of partial sums of independent rv's. Z. Wahrscheinlichkeitstheorie verw. Geb. 35, 213-220. | MR | Zbl

Mori, T. ( 1976); The strong law of large numbers when extreme terms are excluded from sums. Z. Wahrscheinlichkeitstheorie verw. Geb. 36, 189-194. | MR | Zbl

Mori, T. ( 1977); Stability for sums of i.i.d. random variables when extreme terms are excluded. Z. Wahrscheinlichkeitstheorie verw. Geb. 40, 159-167. | MR | Zbl

Nagaev, S.V. ( 1979). Large deviations of sums of independent random variables. Ann. Probab. 7, 745-789. | MR | Zbl

Shao, Q.-M. ( 1989). On a problem of Csörgö and Révész. Ann. Probab. 17(2), 809-812. | MR | Zbl

Shepp, L.A. ( 1964). A limit law concerning moving averages. Ann. Math. Stat. 35(1), 424-428. | MR | Zbl

Stadtmüller, U. ( 1995). On a family of summability methods and one-sided tauberian conditions. J. Math. Anal. Appl. 196, 99-119. | MR | Zbl

Steinebach, J. ( 1978). On a necessary condition for the Erdös-Rényi law of large numbers. Proc. Amer. Math. Soc. 68, 97-100. | MR | Zbl