A note on the almost sure central limit theorem

Citations

Cited by:

1. Wang, Jiang-Feng & Liang, Han-Ying, 2008. "A note on the almost sure central limit theorem for negatively associated fields," Statistics & Probability Letters, Elsevier, vol. 78(13), pages 1964-1970, September.
2. Holzmann, Hajo & Koch, Susanne & Min, Aleksey, 2004. "Almost sure limit theorems for U-statistics," Statistics & Probability Letters, Elsevier, vol. 69(3), pages 261-269, September.
3. Horvath, Lajos & Khoshnevisan, Davar, 1995. "Weight functions and pathwise local central limit theorems," Stochastic Processes and their Applications, Elsevier, vol. 59(1), pages 105-123, September.
4. Kifer, Yuri, 2013. "Strong approximations for nonconventional sums and almost sure limit theorems," Stochastic Processes and their Applications, Elsevier, vol. 123(6), pages 2286-2302.
5. Pelletier, Mariane, 1999. "An Almost Sure Central Limit Theorem for Stochastic Approximation Algorithms," Journal of Multivariate Analysis, Elsevier, vol. 71(1), pages 76-93, October.
6. Berkes, István & Horváth, Lajos, 1996. "Between local and global logarithmic averages," Statistics & Probability Letters, Elsevier, vol. 30(4), pages 369-378, November.
7. István Fazekas & Alexey Chuprunov, 2007. "An Almost Sure Functional Limit Theorem for the Domain of Geometric Partial Attraction of Semistable Laws," Journal of Theoretical Probability, Springer, vol. 20(2), pages 339-353, June.
8. Xu, Feng & Wu, Qunying, 2017. "Almost sure central limit theorem for self-normalized partial sums of ρ−-mixing sequences," Statistics & Probability Letters, Elsevier, vol. 129(C), pages 17-27.
9. Denker, Manfred & Zheng, Xiaofei, 2018. "On the local times of stationary processes with conditional local limit theorems," Stochastic Processes and their Applications, Elsevier, vol. 128(7), pages 2448-2462.
10. Marcus, Michael B. & Rosen, Jay, 1995. "Logarithmic averages for the local times of recurrent random walks and Lévy processes," Stochastic Processes and their Applications, Elsevier, vol. 59(2), pages 175-184, October.
11. Hörmann, Siegfried, 2006. "An extension of almost sure central limit theory," Statistics & Probability Letters, Elsevier, vol. 76(2), pages 191-202, January.
12. Luísa Pereira & Zhongquan Tan, 2017. "Almost Sure Convergence for the Maximum of Nonstationary Random Fields," Journal of Theoretical Probability, Springer, vol. 30(3), pages 996-1013, September.
13. Csáki, E. & Földes, A., 1995. "On the logarithmic average of additive functionals," Statistics & Probability Letters, Elsevier, vol. 22(4), pages 261-268, March.
14. Miao, Yu & Wang, Rujun & Adler, Andre, 2016. "Limit theorems for order statistics from exponentials," Statistics & Probability Letters, Elsevier, vol. 110(C), pages 51-57.
15. Ibragimov, Ildar & Lifshits, Mikhail, 1998. "On the convergence of generalized moments in almost sure central limit theorem," Statistics & Probability Letters, Elsevier, vol. 40(4), pages 343-351, November.
16. Matula, Przemyslaw, 2005. "On almost sure limit theorems for positively dependent random variables," Statistics & Probability Letters, Elsevier, vol. 74(1), pages 59-66, August.
17. Bercu, B., 2004. "On the convergence of moments in the almost sure central limit theorem for martingales with statistical applications," Stochastic Processes and their Applications, Elsevier, vol. 111(1), pages 157-173, May.
18. Mikhail Gordin & Michel Weber, 2002. "On the Almost Sure Central Limit Theorem for a Class of Z d -Actions," Journal of Theoretical Probability, Springer, vol. 15(2), pages 477-501, April.
19. Fahrner, I. & Stadtmüller, U., 1998. "On almost sure max-limit theorems," Statistics & Probability Letters, Elsevier, vol. 37(3), pages 229-236, March.
20. Berkes, István & Horváth, Lajos, 2001. "The logarithmic average of sample extremes is asymptotically normal," Stochastic Processes and their Applications, Elsevier, vol. 91(1), pages 77-98, January.
21. Dudzinski, Marcin, 2003. "A note on the almost sure central limit theorem for some dependent random variables," Statistics & Probability Letters, Elsevier, vol. 61(1), pages 31-40, January.
22. Chen, Shouquan & Lin, Zhengyan, 2008. "Almost sure functional central limit theorems for weakly dependent sequences," Statistics & Probability Letters, Elsevier, vol. 78(13), pages 1683-1693, September.
23. Li, Jingyu & Zhang, Yong, 2021. "An almost sure central limit theorem for the stochastic heat equation," Statistics & Probability Letters, Elsevier, vol. 177(C).
24. Lifshits, M. A. & Stankevich, E. S., 2001. "On the large deviation principle for the almost sure CLT," Statistics & Probability Letters, Elsevier, vol. 51(3), pages 263-267, February.
25. Peligrad, Magda & Shao, Qi-Man, 1995. "A note on the almost sure central limit theorem for weakly dependent random variables," Statistics & Probability Letters, Elsevier, vol. 22(2), pages 131-136, February.
26. Bercu, Bernard & Nourdin, Ivan & Taqqu, Murad S., 2010. "Almost sure central limit theorems on the Wiener space," Stochastic Processes and their Applications, Elsevier, vol. 120(9), pages 1607-1628, August.
27. Wu, Qunying, 2011. "Almost sure limit theorems for stable distributions," Statistics & Probability Letters, Elsevier, vol. 81(6), pages 662-672, June.
28. Zheng, Guangqu, 2017. "Normal approximation and almost sure central limit theorem for non-symmetric Rademacher functionals," Stochastic Processes and their Applications, Elsevier, vol. 127(5), pages 1622-1636.
29. Koval, Valery & Schwabe, Rainer, 2003. "A law of the iterated logarithm for stochastic approximation procedures in d-dimensional Euclidean space," Stochastic Processes and their Applications, Elsevier, vol. 105(2), pages 299-313, June.
30. Rychlik, Zdzislaw & Szuster, Konrad S., 2003. "On strong versions of the central limit theorem," Statistics & Probability Letters, Elsevier, vol. 61(4), pages 347-357, February.
31. Csáki, Endre & Földes, Antónia, 1997. "On the logarithmic average of iterated processes," Statistics & Probability Letters, Elsevier, vol. 33(4), pages 347-358, May.
32. Tabacu, Lucia & Ledbetter, Mark, 2019. "Change-point analysis using logarithmic quantile estimation," Statistics & Probability Letters, Elsevier, vol. 150(C), pages 94-100.
33. Panga, Zacarias & Pereira, Luísa, 2019. "On the almost sure convergence for the joint version of maxima and minima of stationary sequences," Statistics & Probability Letters, Elsevier, vol. 154(C), pages 1-1.
34. Tan, Zhongquan & Peng, Zuoxiang, 2009. "Almost sure convergence for non-stationary random sequences," Statistics & Probability Letters, Elsevier, vol. 79(7), pages 857-863, April.
35. Heck, Matthias K., 1998. "The principle of large deviations for the almost everywhere central limit theorem," Stochastic Processes and their Applications, Elsevier, vol. 76(1), pages 61-75, August.
36. Siegfried Hörmann, 2007. "Critical Behavior in Almost Sure Central Limit Theory," Journal of Theoretical Probability, Springer, vol. 20(3), pages 613-636, September.
37. Alain Rouault & Marc Yor & Marguerite Zani, 2002. "A Large Deviations Principle Related to the Strong Arc-Sine Law," Journal of Theoretical Probability, Springer, vol. 15(3), pages 793-815, July.
38. István Berkes & Siegfried Hörmann & Lajos Horváth, 2010. "On Functional Versions of the Arc-Sine Law," Journal of Theoretical Probability, Springer, vol. 23(1), pages 109-126, March.
39. Giuliano-Antonini, R. & Weber, M., 2008. "The theta-dependence coefficient and an Almost Sure Limit Theorem for random iterative models," Statistics & Probability Letters, Elsevier, vol. 78(5), pages 564-575, April.