@article{TVP_2009_54_4_a15,
author = {T.-X. Pang and Z.-Y. Lin},
title = {On the rates of the {Chung-type} law of logarithm},
journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
pages = {814--828},
year = {2009},
volume = {54},
number = {4},
language = {en},
url = {http://geodesic.mathdoc.fr/item/TVP_2009_54_4_a15/}
}
T.-X. Pang; Z.-Y. Lin. On the rates of the Chung-type law of logarithm. Teoriâ veroâtnostej i ee primeneniâ, Tome 54 (2009) no. 4, pp. 814-828. http://geodesic.mathdoc.fr/item/TVP_2009_54_4_a15/
[1] Baum L. E., Katz M., “Convergence rates in the law of large numbers”, Trans. Amer. Math. Soc., 120 (1965), 108–123 | DOI | MR | Zbl
[2] Billingsley P., Convergence of Probability Measures, Wiley, New York, 1999, 277 pp. | MR | Zbl
[3] Chow Y. S., “On the rate of moment convergence of sample sums and extremes”, Bull. Inst. Math. Acad. Sin., 16:3 (1988), 177–201 | MR | Zbl
[4] Chow Y. S., Lai T. L., “Some one-sided theorems on the tail distribution of sample sums with applications to the last time and largest excess of boundary crossings”, Trans. Amer. Math. Soc., 208 (1975), 51–72 | DOI | MR | Zbl
[5] Ciesielski Z., Taylor S. J., “First passage times and sojourn times for Brownian motion in space and the exact Hausdorff measure of the sample path”, Trans. Amer. Math. Soc., 103 (1962), 434–450 | DOI | MR | Zbl
[6] Csőrgö M., Révész P., Strong Approximations in Probability and Statistics, Academic Press, New York–London, 1981, 284 pp. | MR
[7] Erdős P., “On a theorem of Hsu and Robbins”, Ann. Math. Statist., 20 (1949), 286–291 | DOI | MR | Zbl
[8] Esseen C. G., “On the concentration function of a sum of independent random variables”, Z. Wahrscheinlichkeitstheor. verw. Geb., 9 (1968), 290–308 | DOI | MR | Zbl
[9] Gut A., Spǎtaru A., “Precise asymptotics in the law of the iterated logarithm”, Ann. Probab., 28:4 (2000), 1870–1883 | DOI | MR | Zbl
[10] Gut A., Spǎtaru A., “Precise asymptotics in the Baum–Katz and Davis law of large numbers”, J. Math. Anal. Appl., 248:1 (2000), 233–246 | DOI | MR | Zbl
[11] Hsu P. L., Robbins H., “Complete convergence and the law of large numbers”, Proc. Natl. Acad. Sci. USA, 33 (1947), 25–31 | DOI | MR | Zbl
[12] Lai T. L., “Limit theorems for delayed sums”, Ann. Probab., 2 (1975), 432–440 | DOI | MR
[13] Pang T. X., Lin Z. Y., “Precise rates in the law of logarithm for i.i.d. random variables”, Comput. Math. Appl., 49:7–8 (2005), 997–1010 | DOI | MR | Zbl
[14] Petrov V. V., Limit Theorems of Probability Theory, Clarendon Press, New York, 1995, 292 pp. | MR | Zbl
[15] Rozovskii L. V., “O tochnoi asimptotike v slabom zakone bolshikh chisel dlya summ nezavisimykh sluchainykh velichin s obschei funktsiei raspredeleniya iz oblasti prityazheniya ustoichivogo zakona. I”, Teoriya veroyatn. i ee primen., 48:3 (2003), 589–596 | MR | Zbl
[16] Rozovskii L. V., “O tochnoi asimptotike v slabom zakone bolshikh chisel dlya summ nezavisimykh sluchainykh velichin s obschei funktsiei raspredeleniya iz oblasti prityazheniya ustoichivogo zakona. II”, Teoriya veroyatn. i ee primen., 49:4 (2004), 803–813 | MR | Zbl
[17] Sakhanenko A. I., “Ob otsenkakh skorosti skhodimosti v printsipe invariantnosti”, Predelnye teoremy teorii veroyatnostei i smezhnye voprosy, Tr. In-ta matematiki, 1, Nauka, Novosibirsk, 1982; Sakhanenko A. I., “On estimates of the rate of convergence in the invariance principle”, Advances in Probability Theory: Limit Theorems and Related Problems, ed. A. A. Borovkov, Optimization Software, New York, 1984, 124–135
[18] Sakhanenko A. I., “Convergence rate in the invariance principle for nonidentically distributed variables with exponential moments”, Advances in Probability Theory: Limit Theorems for Sums of Random Variables, ed. A. A. Borovkov, Optimization Software, New York, 1986, 2–73
[19] Spǎtaru A., “Precise asymptotics in Spitzer's law of large numbers”, J. Theoret. Probab., 12:3 (1999), 811–819 | DOI | MR
[20] Zhang L. X., On the rates of the other law of the logarithm, arXiv:math.PR/0610521
[21] Zhang L. X., “Some limit results on the law of the iterated logarithm for NA sequences”, Acta Math. Sinica (Chin. Ser.), 47:3 (2004), 541–552 (In Chinese) | MR | Zbl