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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.
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참고문헌 (24)
참고문헌 신청
A. Dembinska / 2007 / How many observations fall in a neighborhood of an order statistic? / Comm. Statist. Theory Methods 36 (5-8) : 851 ~ 867
A. Stepanov / 2011 / On the Borel-Cantelli Lemma / Comment. Math. Univ. Carolin 8 (4) : 211 ~ 216
B. L. S. Prakasa Rao / 2009 / Conditional independence, conditional mixing and conditional association / Ann. Inst. Statist. Math 61 (2) : 441 ~ 460
C. Feng / 2009 / On the Borel-Cantelli Lemma and its generalization / C. R. Math. Acad. Sci. Paris 347 (21-22) : 1313 ~ 1316
D. Majerek / 2005 / Conditional strong law of large number / Int. J. Pure Appl. Math 20 (2) : 143 ~ 156
A. Stepanov / 2011 / On the Borel-Cantelli Lemma / Comment. Math. Univ. Carolin 8 (4) : 211 ~ 216
B. L. S. Prakasa Rao / 2009 / Conditional independence, conditional mixing and conditional association / Ann. Inst. Statist. Math 61 (2) : 441 ~ 460
C. Feng / 2009 / On the Borel-Cantelli Lemma and its generalization / C. R. Math. Acad. Sci. Paris 347 (21-22) : 1313 ~ 1316
D. Majerek / 2005 / Conditional strong law of large number / Int. J. Pure Appl. Math 20 (2) : 143 ~ 156
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