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THE CONDITIONAL BOREL-CANTELLI LEMMA AND APPLICATIONS

Qianmin Chen|Jicheng Liu
대한수학회 (The Korean Mathematical Society)|2017.03|대한수학회지 (Journal of the KMS)|제54권 제2호|pp. 441-460

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키워드

order statisticsconditional independenceconditional Borel-Cantelli lemmaconcomitant
주제분류수학

초록

In this paper, we establish some conditional versions of the first part of the Borel-Cantelli lemma. As its applications, we study strong limit results of $\sF$-independent random variables sequences, the convergence of sums of $\sF$-independent random variables and the conditional version of strong limit results of the concomitants of order statistics.

Abstract

In this paper, we establish some conditional versions of the first part of the Borel-Cantelli lemma. As its applications, we study strong limit results of $\sF$-independent random variables sequences, the convergence of sums of $\sF$-independent random variables and the conditional version of strong limit results of the concomitants of order statistics.

참고문헌 (24)

  1. Modelling the dependence structure of financial assets: a survey of four copulas, "K. Aas", Norsk Regnesentral, ~, pp.Technical Report SAMBA (2004), 22[DOI]
  2. I. Bairamov, "Numbers of near bivariate record-concomitant observations", J. Multivariate Anal, 102(5), pp.908~917 (2011)
  3. N. Balakrishnan, "Limit results for concomitants of order statistics", Metrika, 78(4), pp.385~397 (2015)
  4. I. V. Basawa, "Asymptotic Optimal Inference for Non-Ergodic Models" (1983), Springer-Verlag
  5. P. K. Bhattacharya, "Nonparametric methods", pp.383~403 (1984), North-Holland
  6. T. K. Chandra, "The Borel-Cantelli Lemma under dependence conditions", Statist. Probab. Lett, 78(4), pp.390~395 (2008)
  7. T. C. Christofides, "Conditional demimartingales and related results", J. Math. Anal. Appl, 398(1), pp.380~391 (2013)
  8. A. Dembinska, "How many observations fall in a neighborhood of an order statistic?", Comm. Statist. Theory Methods, 36(5-8), pp.851~867 (2007)
  9. C. Feng, "On the Borel-Cantelli Lemma and its generalization", C. R. Math. Acad. Sci. Paris, 347(21-22), pp.1313~1316 (2009)
  10. J. Liu, "A note on the bilateral inequality for a sequence of random variables", Statist. Probab. Lett, 82(5), pp.871~875 (2012)
  11. J. Liu, "On conditional Borel-Cantelli lemmas for sequences of random variables", J. Math. Anal. Appl, 399(1), pp.156~165 (2013)
  12. J. C. Liu, "Conditional Borel-Cantelli Lemma and conditional strong law of large number", Acta Math. Appl. Sin, 37(3), pp.537~546 (2014)
  13. D. Majerek, "Conditional strong law of large number", Int. J. Pure Appl. Math, 20(2), pp.143~156 (2005)
  14. T. F. Mori, "On the Erdos-Renyi generalization of the Borel-Cantelli lemma", Studia Sci. Math. Hungar, 18(2-4), pp.173~182 (1983)
  15. M. Ordonez Cabrera, "Some theorems on conditional mean convergence and conditional almost sure convergence for randomly weighted sums of dependent random variables", TEST, 21(2), pp.369~385 (2012)
  16. V. V. Petrov, "A note on the Borel-Cantelli Lemma", Statist. Probab. Lett, 58(3), pp.283~286 (2002)
  17. V. V. Petrov, "A generalization of the Borel-Cantelli Lemma", Statist. Probab. Lett, 67(3), pp.233~239 (2004)
  18. B. L. S. Prakasa Rao, "Conditional independence, conditional mixing and conditional association", Ann. Inst. Statist. Math, 61(2), pp.441~460 (2009)
  19. G. G. Roussas, "On conditional independence, mixing, and association", Stoch. Anal. Appl, 26(6), pp.1274~1309 (2008)
  20. A. Stepanov, "On the Borel-Cantelli Lemma", Comment. Math. Univ. Carolin, 8(4), pp.211~216 (2011)
  21. X. H. Wang, "Some inequalities for conditional demimartingales and conditional N-demimartingales", Statist. Probab. Lett, 83(3), pp.700~709 (2013)
  22. D. Yuan, "From conditional independence to conditionally negative association:some preliminary results", Comm. Statist. Theory Methods, 44(18), pp.3942~3966 (2015)
  23. De-Mei Yuan, "Conditional central limit theorems for a sequence of conditional independent random variables", 대한수학회지, 51(1), pp.1~15 (2014), 대한수학회
  24. D. Yuan, "Conditional versions of limit theorems for conditionally associated random variables", J. Math. Anal. Appl, 376(1), pp.282~293 (2011)

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