References
- T. Birkel, A Functional Central Limit Theorem for Positively Dependent Random Variables, J. Multivariate Anal. 44 (1993), no. 2, 314-320. https://doi.org/10.1006/jmva.1993.1018
-
Y. K. Choi and M. Csorgo, Path properties of
$l^{p}$ -valued Gaussian random fields, Sci. China Ser. A: Math. 50 (2007), 1501-1520. https://doi.org/10.1007/s11425-007-0084-6 - Y. K. Choi and M. Csorgo, Limsup results and LIL for partial sum processes of a Gaussian random field, Acta Math. Sinica. 24 (2008), no. 9, 1497-1506. https://doi.org/10.1007/s10114-008-6205-5
- Y. K. Choi, K. S. Hwang, T. S. Kim, Z. Y. Lin and W. S. Wang, Asymptotic behaviors for partial sum processes of a Gaussian sequence, Acta Math. Hungar. 103 (2004), 43-54. https://doi.org/10.1023/B:AMHU.0000028235.82111.cf
-
M. Csorgo, Z. Y. Lin, and Q. M. Shao, Path properties for
$l^{{\infty}}$ -valued Gaussian processes, Proc. Amer. Math. Soc. 121 (1994), 225-236. - M. Csorgo and P. Revesz, Strong Approximations in Probability and Statistics, Academic Press, New York, 1981.
- M. Csorgo and P. Revesz, How big are the increments of a Wiener process? Ann. Probab. 7 (1979), 731-737. https://doi.org/10.1214/aop/1176994994
- M. Csorgo and P. Revesz , How small are the increments of a Wiener process? Stochastic Process Appl. 8 (1979), 119-129.
- M. Csorgo and J. Steinebach, Improved Erdos-Renyi and strong approximation laws for increments of partial sums, Ann. Probab. 9 (1981), no. 6, 988-996. https://doi.org/10.1214/aop/1176994269
- P. Deheuvels and J. Steinebach, Exact convergence rates in strong approximation laws for large increments of partial sums, Probab. Theory Related Fields 76 (1987), 369-393. https://doi.org/10.1007/BF01297492
- P. Erdos and A. Renyi, On a new law of large numbers, J. Analyse Math. 13 (1970), 103-111.
- J. Esary, F. Proschan and D.Walkup, Association of random variables with applications, Ann. Math. Statist. 38 (1967), no. 4, 1466-1474. https://doi.org/10.1214/aoms/1177698701
- K. Joag-Dev, Independence via uncorrelatedness under certain dependence structures, Ann. Probab. 11 (1983), no. 4, 1037-1041. https://doi.org/10.1214/aop/1176993452
- K. Joag-Dev and F. Proschan, Negative association of random variables with applications, Ann. Statist. 11 (1983), no. 1, 286-295. https://doi.org/10.1214/aos/1176346079
- H. Lanzinger and U. Stadtmuller, Maxima of increments of partial sums for certain subexponential distributions, Stochastic Process. Appl. 86 (2000), 307-322. https://doi.org/10.1016/S0304-4149(99)00100-3
- E. L. Lehmann, Some concepts od dependence, Ann. Math. Statist. 37 (1966), no. 5, 1137-1153. https://doi.org/10.1214/aoms/1177699260
- Y. X. Li and J. F. Wang, The law of the iterated logarithm for positively dependent random variables, J. Math. Anal. Appl. 339 (2008), no. 1, 259-265. https://doi.org/10.1016/j.jmaa.2007.06.044
- Z. Y. Lin, On Csorgo-Revesz's increments of sums of non-i.i.d. random variables, Scientia Sinica (Series A) 30 (1987), 921-931.
-
Z. Y. Lin, On the increments of partial sums of
${\phi}$ -mixing sequence, Teor. Veroyatnost. i Primenen. 36 (1991), 326-336; translation in Theory Probab. Appl. 36 (1992), 316-328. -
Z. Y. Lin, S. H. Lee, K. S. Hwang and Y. K. Choi, Some limit theorems on the increments of
$l^{p}$ -valued multi-parameter Gaussian processes, Acta Math. Sinica, English Ser. 20 (2004), no. 6, 1019-1028. https://doi.org/10.1007/s10114-004-0414-3 - Z. Y. Lin and C. R. Lu, Strong Limit Theorems, New York, 1975.
- Z. Y. Lin, C. R. Lu and L. X. Zhang, Path Properties of Gaussian Processes, Zhejiang University Press, 2001.
- C. M. Newman, Normal fluctuations and the FKG inequalities, Comm. Math. Phys. 74 (1980), no. 2, 119-128. https://doi.org/10.1007/BF01197754
- C. M. Newman, Asymptotic independence and limit theorems for positively and negatively dependent random variables, in: Inequalities in Statistics and Probability (Tong Y. L., Ed., Institute of Mathematical Statistics, Hayward, CA) (1984), 127-140.
- V. V. Petrov, Sums of Independent Random Variables, Springer-Verlag, New York, 1975.
- J. F. Wang and L. X. Zhang, A Berry-Esseen theorem for weakly negatively dependent random variables and its applications, Acta Math. Hungar. 110 (2006), no, 4, 293-308. https://doi.org/10.1007/s10474-006-0024-x
- Y. Yang and Y. B. Wang, The asymptotical normality of the renewal process generated by strictly stationary LPQD sequences, Chinese J. Appl. Probab. Statist. 24 (2008), no. 1, 37-42.
- L. X. Zhang, Central limit theorems for asymptotically negatively associated random fields, Acta Math. Sinica, Engl. Ser. 16 (2000), no. 4, 691-710. https://doi.org/10.1007/s101140000084