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THE LIMIT THEOREMS UNDER LOGARITHMIC AVERAGES FOR MIXING RANDOM VARIABLES
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 Title & Authors
THE LIMIT THEOREMS UNDER LOGARITHMIC AVERAGES FOR MIXING RANDOM VARIABLES
Zhang, Yong;
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 Abstract
In this paper, under some suitable integrability and smoothness conditions on f, we establish the central limit theorems for , where is the partial sums of strictly stationary mixing random variables with $EX_1
 Keywords
central limit theorem;almost sure central limit theorem;logarithmic averages;mixing random variables;
 Language
English
 Cited by
 References
1.
I. Berkes, X. Chen, and L. Horvath, Central limit theorems for logarithm averages, Studia Sci. Math. Hungar. 38 (2001), 79-96.

2.
I. Berkes, E. Csaki, and L. Horvath, Almost sure central limit theorems under minimal conditions, Statist. Probab. Lett. 37 (1998), no. 1, 67-76. crossref(new window)

3.
I. Berkes and L. Horvath, Almost sure invariance principles for logarithmic averages, Studia Sci. Math. Hungar. 33 (1997), no. 1-3, 1-24.

4.
G. A. Brosamler, An almost everywhere central limit theorem, Math. Proc. Cambridge Philos. Soc. 104 (1988), no. 3, 561-574. crossref(new window)

5.
M. Csorgo and L. Horvath, Invariance principles for logarithmic averages, Math. Proc. Cambridge Philos. Soc. 112 (1992), no. 1, 195-205. crossref(new window)

6.
L. Horvath and D. Khoshnevisan, Weight functions and pathwise local central limit theorems, Stochastic Process. Appl. 59 (1995), no. 1, 105-123. crossref(new window)

7.
L. Horvath and D. Khoshnevisan, A strong approximation for logarithmic averages, Studia Sci. Math. Hungar. 31 (1996), no. 1-3, 187-196.

8.
I. A. Ibragimov, Some limit theorems for stationary process, Theory Probab. Appl. 7 (1962), 349-382. crossref(new window)

9.
I. Ibragimov and M. Lifshits, On the convergence of generalized moments in almost sure central limit theorem, Statist. Probab. Lett. 40 (1998), no. 4, 343-351. crossref(new window)

10.
A. N. Kolmogorov and Y. A. Rozanov, On strong mixing conditions for stationary Gaussian processes, Theory Probab. Appl. 5 (1960), no. 2, 204-208. crossref(new window)

11.
M. Lacey and W. Philipp, A note on the almost sure central limit theorem, Statist. Probab. Lett. 9 (1990), no. 3, 201-205. crossref(new window)

12.
S. P. Meyn and R. L. Tweedie, Markov Chains and Stochastic Stability, Springer, London, 1993.

13.
M. Rosenblatt, A central limit theorem and a strong mixing condition, Proc. Nat. Acad. Sci. USA 42 (1956), 43-47. crossref(new window)

14.
P. Schatte, On strong versions of the central limit theorem, Math. Nachr. 137 (1988), 249-256. crossref(new window)

15.
Q. M. Shao, Almost sure invariance principles for mixing sequences of random variables, Stochastic Process. Appl. 48 (1993), no. 2, 319-334. crossref(new window)

16.
Q. M. Shao and C.R. Lu, Strong approximations for partial sums of weakly dependent random variables, Sci. Sinica. Ser. A 30 (1987), no. 6, 575-587.