본문 바로가기
KERD
논문KCI 등재

The limit theorems under logarithmic averages for mixing random variables

Yong Zhang
대한수학회 (The Korean Mathematical Society)|2014.04|대한수학회논문집 (Communications of the KMS)|제29권 제2호|pp. 351-358

2

조회

0

다운로드

0

인용

0

참고문헌

키워드

central limit theoremalmost sure central limit theoremlogarithmic averagesmixing random variables
주제분류수학

초록

In this paper, under some suitable integrability and smoothness conditions on f, we establish the central limit theorems for ∑ k≤N k−1f(Sk/σ√k), where Sk is the partial sums of strictly stationary mixing random variables with EX1 = 0 and σ2 = EX2 1 +2∑∞ k=1 EX1X1+k. We also establish an almost sure limit behaviors of the above sums.

Abstract

In this paper, under some suitable integrability and smoothness conditions on f, we establish the central limit theorems for ∑ k≤N k−1f(Sk/σ√k), where Sk is the partial sums of strictly stationary mixing random variables with EX1 = 0 and σ2 = EX2 1 +2∑∞ k=1 EX1X1+k. We also establish an almost sure limit behaviors of the above sums.

참고문헌 (16)

  1. I. Berkes, "Central limit theorems for logarithm averages", Studia Sci. Math. Hungar, 38, pp.79~96 (2001)
  2. I. Berkes, "Almost sure central limit theorems under minimal conditions", Statist. Probab. Lett, 37(1), pp.67~76 (1998)
  3. I. Berkes, "Almost sure invariance principles for logarithmic averages", Studia Sci. Math. Hungar, 33(1-3), pp.1~24 (1997)
  4. G. A. Brosamler, "An almost everywhere central limit theorem", Math. Proc. Cambridge Philos. Soc, 104(3), pp.561~574 (1988)
  5. M. Csorgo, "Invariance principles for logarithmic averages", Math. Proc. Cambridge Philos. Soc, 112(1), pp.195~205 (1992)
  6. L. Horvath, "Weight functions and pathwise local central limit theorems", Stochastic Process. Appl, 59(1), pp.105~123 (1995)
  7. L. Horvath, "A strong approximation for logarithmic averages", Studia Sci. Math. Hungar, 31(1-3), pp.187~196 (1996)
  8. I. A. Ibragimov, "Some limit theorems for stationary process", Theory Probab. Appl, 7, pp.349~382 (1962)
  9. I. Ibragimov, "On the convergence of generalized moments in almost sure central limit theorem", Statist. Probab. Lett, 40(4), pp.343~351 (1998)
  10. A. N. Kolmogorov, "On strong mixing conditions for stationary Gaussian processes", Theory Probab. Appl, 5(2), pp.204~208 (1960)
  11. M. Lacey, "A note on the almost sure central limit theorem", Statist. Probab. Lett, 9(3), pp.201~205 (1990)
  12. S. P. Meyn, "Markov Chains and Stochastic Stability" (1993), Springer
  13. M. Rosenblatt, "A central limit theorem and a strong mixing condition", Proc. Nat. Acad. Sci. USA, 42, pp.43~47 (1956)
  14. P. Schatte, "On strong versions of the central limit theorem", Math. Nachr, 137, pp.249~256 (1988)
  15. Q. M. Shao, "Almost sure invariance principles for mixing sequences of random variables", Stochastic Process. Appl, 48(2), pp.319~334 (1993)
  16. Q. M. Shao, "Strong approximations for partial sums of weakly dependent random variables", Sci. Sinica. Ser. A, 30(6), pp.575~587 (1987)

관련 논문AI추천

SELF-NORMALIZED WEAK LIMIT THEOREMS FOR A φ-MIXING SEQUENCE문희진, 최용갑대한수학회 · 대한수학회보2010 · 제47권 제6호Central limit theorems for conditionally strong mixing and conditionally strictly stationary sequences of random variablesDe-Mei Yuan, Xiao-Lin Zeng대한수학회 · 대한수학회지2024 · 제61권 제4호PRECISE ASYMPTOTICS FOR THE MOMENT CONVERGENCE OF MOVING-AVERAGE PROCESS UNDER DEPENDENCEKe-Ang Fu, Qing-Pei Zang대한수학회 · 대한수학회보2010 · 제47권 제3호PRECISE ASYMPTOTICS OF MOVING AVERAGE PROCESS UNDER Φ-MIXING ASSUMPTIONJie Li대한수학회 · 대한수학회지2012 · 제49권 제2호A strong limit theorem for sequences of blockwise and pairwise m-dependent random variablesNgoc Anh Vu, Van Thanh Le대한수학회 · 대한수학회보2011 · 제48권 제2호Weak laws of large numbers for arrays under a condition of uniform integrability성수학, Andrei Volodin, Supranee Lisawadi대한수학회 · 대한수학회지2008 · 제45권 제1호

이 간행물의 다른 논문 (15건)

HILBERT 2-CLASS FIELD TOWERS OF REAL QUADRATIC FUNCTION FIELDS정환엽pp. 219-226Nonnegative integral matrices having generalized inversesSEOK-ZUN SONG, 강경태, LeRoy B. Beasley, Luis Hernandez Encinaspp. 227-237Shifted harmonic sums of order twoAnthony Sofopp. 239-255Generalized Riesz points for perturbations of Toeplitz operators김안현pp. 257-262On the growth rate of solutions to Gross-Neveu and Thirring equations허형진pp. 263-267
원문 보기