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Amghibech, S. , On the Borel-Cantelli Lemma and moments, Comment. Math. Univ. Carolin. , 47 (2006), 669–679. Amghibech S. On

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Chandra, T. K. , The Borel-Cantelli lemma , Springer, Heidelberg, 2012. Chandra T. K. The Borel-Cantelli lemma 2012

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Abstract  

We establish strong limsup theorems related to the law of the iterated logarithm (LIL) for finite dimensional Gaussian random fields by using the second Borel-Cantelli lemma.

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References [1] Chung , K. and Erdős , P. , On the application of the Borel-Cantelli lemma , Trans. Amer. Math. Soc. , 72 ( 1952 ), 179 - 186

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Moment inqualities and strong laws of large numbers are proved for random allocations of balls into boxes. Random broken lines and random step lines are constructed using partial sums of i.i.d. random variables that are modified by random allocations. Functional limit theorems for such random processes are obtained.

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