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ALMOST SURE CONVERGENCE OF WEIGHTED SUMS FOR WIDELY NEGATIVE DEPENDENT RANDOM VARIABLES UNDER SUB-LINEAR EXPECTATIONS

황교신
장전수학회 (Jangjeon Mathematical Society)|2022.10|Advanced Studies in Contemporary Mathematics|제32권 제4호|pp. 463-475

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참고문헌

키워드

sub-linear expectationnonlinear expectationalmost sure convergencewidely negative dependenceweighted sumsEND random variable
주제분류수학

초록

The sub-linear expectation space is a nonlinear expectation space having advantages of modeling the uncertainty of probability and statistics. In this paper we study the almost sure convergence for weighted sums of widely negative dependent random variables in the sub-linear expectation spaces. An almost sure convergence theorem is obtained for weighted sums of widely negative dependent random variables under sub-linear expectations. Our results extend and generalize the corresponding ones of Hu and Wu(2021) to widely negative dependent random variables under sub-linear expectation.

Abstract

The sub-linear expectation space is a nonlinear expectation space having advantages of modeling the uncertainty of probability and statistics. In this paper we study the almost sure convergence for weighted sums of widely negative dependent random variables in the sub-linear expectation spaces. An almost sure convergence theorem is obtained for weighted sums of widely negative dependent random variables under sub-linear expectations. Our results extend and generalize the corresponding ones of Hu and Wu(2021) to widely negative dependent random variables under sub-linear expectation.

참고문헌 (22)

  1. Z.J. Chen, "Strong lasw of large numbers for sub-linear expectation", Sci. China Math, 59(5), pp.945~954 (2016)
  2. Zengjing Chen, "A law of the iterated logarithm under sublinear expectations", Journal of Financial Engineering, 01(02), pp.1450015~ (2014), World Scientific Pub Co Pte Lt[DOI]
  3. H. Cheng, "A strong law of large numbers for sub-linear under a general moment condition", Stat. & Probab. Lett, 116, pp.248~258 (2016)
  4. C. Hu, "Strong laws of large numbers for sublinear expectation under controlled 1st moment condition", Chines Ann Math. Ser. B, 39(5), pp.791~804 (2019)
  5. R. Hu, "Almost sure convergence of weighted sums for END sequences in sub-linear expectation spaces", J. Jilin Univ, 59(3), pp.531~536 (2021)
  6. 황교신, "Note on Strong Law of Large Number under Sub-linear Expectation", East Asian Mathematical Journal, 36(1), pp.25~34 (2020), 영남수학회
  7. 황교신, "A NOTE ON STRONG CONVERGENCE OF SUMS OF INDEPENDENT RANDOM VARIABLES UNDER SUB-LINEAR EXPECTATION", Advanced Studies in Contemporary Mathematics, 30(3), pp.435~445 (2020), 장전수학회
  8. Y. Lin, "Complete convergence and strong law of large numbers for arrays of random variables under sublinear expectations", Communications in Statistics-Theory & Methods, 49(23), pp.5866~5882 (2020)
  9. M. Marinacci, "Limit laws for non-additive probabilities and their frequentist interpretation", J. Econom, Theory, 84, pp.145~195 (1999)
  10. S.G. Peng, "G-expectation, G-Brownian motion and related stochastic calculus of Ito type", Stoch. Anal. Appli., Proceedings of the 2005 Abel Symposium, pp.541~567 (2005), Springer
  11. "2010", ~
  12. S.G. Peng, "A new central limit theorem under sublinear expectations", J. Math., 53(8), pp.1989~1994 (2008)
  13. S.G. Peng, "Survey on normal distributions, central limit theorem, Brownian motion and the related stochastic calculus under sublinear expectations", Sci. China Ser. A:Math, 52(7), pp.1391~1411 (2009)
  14. S.G. Peng, "Law of large numbers and central limit theorem under nonlinear expectations", Probab., Uncertain. & Quanti. risk, 4(4), pp.1~8 (2019)
  15. Q. Wu, "Strong law of large numbers and Chover’s law of the iterated logarithm under sub-linear expectations", J. Math. Anal. Appl, 460(1), pp.252~270 (2018)
  16. Q. Wu, "Another form of Chover’s law of the iterated logarithm under sublinear expectations, Revista de la Real Academia de Ciencias Exactas", Fsicas y Naturales, Serie A. Matematicas, 114(1) (2020)
  17. Z. Zhan, "Strong laws of large numbers for weighted sums of extended negatively dependent random variables under sub-linear expectations", Communications in Statistics-Theory & Methods, 51(5), pp.1197~1216 (2022)
  18. L.X. Zhang, "Donsker’s invariance principle under the sub-linear expectation with an application to Chung’s law of the iterated logarithm", Commun. Math. Stat., 3, pp.187~214 (2015)
  19. L.X. Zhang, "Exponential inequalities under the sub-linear expectations with applications to laws the iterated logarithm", Sci. China Math., 59(12), pp.2503~2526 (2016)
  20. L.X. Zhang, "Rosenthal’s inequalities for independent and negatively dependent random variables under sub-linear expectations with applications", Sci. China Math., 59(4), pp.751~768 (2016)
  21. L.X. Zhang, "Self-normalized moderate deviation and laws of the iterated logarithm under g-expectation", Commun. Math. & Stati., 4, pp.229~263 (2016)
  22. L.X. Zhang, "Strong limit theorems for extended independent and extended negatively dependent random variables under non-linear expectations", Acta Mathematica Scientia, 42, pp.467~490 (2022)

관련 논문AI추천

Complete $f$-moment convergence for extended negatively dependent random variables under sub-linear expectationsChao Lu, Rui Wang, Xuejun Wang, Yi Wu대한수학회 · 대한수학회지2020 · 제57권 제6호Note on complete convergence for weighted sums of widely negative dependent random variables under sub-linear expectationsKyo-Shin Hwang장전수학회 · Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집)2025 · 제28권 제1호A NOTE ON STRONG CONVERGENCE OF SUMS OF INDEPENDENT RANDOM VARIABLES UNDER SUB-LINEAR EXPECTATION황교신장전수학회 · Advanced Studies in Contemporary Mathematics2020 · 제30권 제3호On complete convergence for extended independent random variables under sub-linear expectationsXin Deng, Xuejun Wang대한수학회 · 대한수학회지2020 · 제57권 제3호ON A SPITZER-TYPE LAW OF LARGE NUMBERS FOR PARTIAL SUMS OF INDEPENDENT AND IDENTICALLY DISTRIBUTED RANDOM VARIABLES UNDER SUB-LINEAR EXPECTATIONSMiaomiao Wang, Min Wang, Xuejun Wang대한수학회 · 대한수학회보2023 · 제60권 제3호Note on Strong Law of Large Number under Sub-linear Expectation황교신영남수학회 · East Asian Mathematical Journal2020 · 제36권 제1호

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