Limsup results for the increments of partial sums of a random sequence
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Let {xi_j ; j >= 1} be a centered strictly stationary random sequence defined by S_0 = 0; S_n = sum_^n_{j=1} xi_j and sigma(n) = sqrt{ES^2_n}, where sigma(t), t > 0, is a nondecreasing continuous regularly varying function. Suppose that there exists n_0 >= 1 such that, for any n >= n_0 and 0 <= xi < 1, there exist positive constants c_1 and c_2 such that c_1 e^{−(1+ epsilon)x_2/2} <= P {|Sn| /sigma(n) >= x_o } <= c2 e^{−(1−epsilon)x^2/2}; x >= 1. Under some additional conditions, we investigate some limsup results for the increments of partial sum processes of the sequence {xi_j ; j >= 1}.
Abstract
Let {xi_j ; j >= 1} be a centered strictly stationary random sequence defined by S_0 = 0; S_n = sum_^n_{j=1} xi_j and sigma(n) = sqrt{ES^2_n}, where sigma(t), t > 0, is a nondecreasing continuous regularly varying function. Suppose that there exists n_0 >= 1 such that, for any n >= n_0 and 0 <= xi < 1, there exist positive constants c_1 and c_2 such that c_1 e^{−(1+ epsilon)x_2/2} <= P {|Sn| /sigma(n) >= x_o } <= c2 e^{−(1−epsilon)x^2/2}; x >= 1. Under some additional conditions, we investigate some limsup results for the increments of partial sum processes of the sequence {xi_j ; j >= 1}.
참고문헌 (20)
- Y. K. Choi, "Asymptotic behaviors for the increments of Gaussian random fields", J. Math. Anal. Appl, 246, pp.557~575 (2000)
- T. C. Christofides, "A connection between supermodular ordering and positive", negative association, 2004, pp.88, 138~151
- M. Cs¨org˝o, "Strong Approximations in Probability and Statistics" (1981), Academic Press
- M. Cs¨org˝o, "Donsker’s theorem for self-normalized partial sums processes", Ann. Probab, 31(3), pp.1228~1240 (2003)
- J. D. Esary, "Association of random variables with applications", Ann. Math. Statist, 38, pp.1466~1474 (1967)
- W. Feller, "An Introduction to Probability Theory and Its Applications, Vol. 1" (1968), Wiley
- T. Hu, "Negatively superadditive dependence of random variables with applications", Chinese J. Appl. Statist, 16, pp.133~144 (2000)
- K. Joag-Dev, "Negative association of random variables with applica-tions", Ann. Statist, 11, pp.286~295 (1983)
- Z. Y. Lin, "Strong Limit Theorems" (1992), Kluwer Academic
- Z. Y. Lin, "Path Properties of Gaussian Processes" (2001), Zhejiang University Press
- C. M. Newman, "Asymptotic independence and limit theorems for positively and neg-atively dependent random variables", Ineq. in Statist. Probab., IMS Lecture Notes, 5, pp.127~140 (1984)
- C. M. Newman, "An invariance principle for certain dependent se-quences", Ann. Probab, 9, pp.671~675 (1981)
- R. F. Patterson, "Limit theorems for negatively dependent random variables", Nonlinear Anal, 47, pp.1283~1295 (2001)
- M. Peligrad, "A note on estimation of variance for ½-mixing sequences", Statist. Probab. Lett, 26, pp.141~145 (1996)
- M. Peligrad, "Maximum of partial sums and an invariance principle for a class of weak dependent random variables", Proc. Amer. Math. Soc, 126, pp.1181~1189 (1998)
- M. Peligrad, "Estimation of the variance of partial sums for ½-mixing random variables", J. Multivariate Anal, 52, pp.140~157 (1995)
- G. G. Roussas, "Exponential probability inequalities with some applications, Statist. Probab. Game Theory", pp.303~319 (1996), IMS
- Q. M. Shao, "Self-normalized large deviations", Ann. Probab, 25(1), pp.285~328 (1997)
- C. Su, "The moment inequalities and weak convergence for negatively associated sequences", Sci. China, 40A, pp.172~182 (1997)
- L. X. Zhang, "Self-normalized central limit theorem and estimation of variance of partial sums for negative dependent random variables", Appl. Math. J. Chinese Univ. Ser. B, 17(3), pp.326~334 (2002)