References
- S. A. Book and T. R. Shore, On large intervals in the Csörgő-Révész theorem on increments of a Wiener process, Z. Wahrsch. Verw. Gebiete 46 (1978), 1–11. https://doi.org/10.1007/BF00535684
- Y. K. Choi, Erdös-Rényi-type laws applied to Gaussian processes, J. Math. Kyoto Univ. 31(1) (1991), 191–217. https://doi.org/10.1215/kjm/1250519901
- Y. K. Choi, Z. Y. Lin, W. S. Wang, K. S. Hwang and T. S. Kim, Asymptotic behaviors for partial sum processes of a Gaussian sequence, Acta Math. Hungar. 103(1-2) (2004), 43–54. https://doi.org/10.1023/B:AMHU.0000028235.82111.cf
- E. Csaki and K. Gonchigdanzan, Almost sure limit theorems for the maximum of stationary Gaussian sequences, Statist. Probab. Lett. 58 (2002), 195–203. https://doi.org/10.1016/S0167-7152(02)00128-1
- M. Csorgo, A glimpse of Pál Erdös's impact on probability and statistics, Canad. J. Statist. 30(4) (2002). https://doi.org/10.2307/3316095
- M. Csorgo and P. Revesz, Strong Approximations in Probability and Statistics, Academic Press, New York, 1981.
- M. Csorgo and J. Steinebach, Improved Erdös-Rényi and strong approximation laws for increments of partial sums, Ann. Probab. 9(6) (1981), 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
- A. N. Frolov, On one-sided strong laws for large increments of sums, Statist. Probab. Lett. 37 (1998), 155–165. https://doi.org/10.1016/S0167-7152(97)00113-2
- L. Horvath and Q. M. Shao, Darling-Erdös-type theorems for sums of Gaussian variables with long-range dependence, Stochastic Process. Appl. 63 (1996), 117–137. https://doi.org/10.1016/0304-4149(96)00053-1
- 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
- M. R. Leadbetter, G. Lindgren and H. Rootzen, Extremes and Related Properties of Random Sequences and Processes, Springer-Verlag, New York, 1983.
- W. V. Li and Q. M. Shao, A normal comparison inequality and its applications, Probab. Theory Related Fields 122 (2002), 494–508. https://doi.org/10.1007/s004400100176
- Z. Y. Lin, Path properties of Gaussian processes, Zhejiang University Press, 2001.
- Z. Y. Lin, On Csörgő-Révész's increments of sums of non-i.i.d. random variables, Scientia Sinica (Series A) 30 (1987), no. 9, 921–931.
- Z. Y. Lin, On increments of sums of independent non-identically distributed random variables, Scientia Sinica (Series A) 31 (1988), no. 8, 927–937.
- Z. Y. Lin, Y. K. Choi and K. S. Hwang, Some limit theorems on the increments of a multi-parameter fractional Brownian motion, Stochastic Anal. Appl. 19 (2001), no. 4, 499–517. https://doi.org/10.1081/SAP-100002099
- Z. Y. Lin and Q. M. Shao, On the limiting behaviors of increments of sums of random variables without moment conditions, Chinese Ann. Math. 14B (1993), no. 3, 307–318.
- J. Steinebach, On the increments of partial sum processes with multidimensional indices, Z. Wahrsch. Verw. Gebiete 63 (1983), 59–70. https://doi.org/10.1007/BF00534177
- J. Steinebach, Improved Erdos-Renyi and strong approximation laws for increments of renewal processes, Ann. Probab. 14 (1986), no. 2, 547–559. https://doi.org/10.1214/aop/1176992530
- W. S. Wang, Self-normalized lag increments of partial sums, Statist. Probab. Lett. 58 (2002), 41–51. https://doi.org/10.1016/S0167-7152(02)00101-3