Some Lil Type Results on the Partial Sums and Trimmed Sums with Multidimensional Indices
نویسنده
چکیده
Let {X,Xn;n ∈ N} be a field of i.i.d. random variables indexed by d-tuples of positive integers and let Sn = ∑ k≤n Xk. We prove some strong limit theorems for Sn. Also, when d ≥ 2 and h(n) satisfies some conditions, we show that there are no LIL type results for Sn/ √ |n|h(n).
منابع مشابه
CHOVER-TYPE LAWS OF THE ITERATED LOGARITHM FOR WEIGHTED SUMS OF rhoast-MIXING SEQUENCES
We call this a Chover-type LIL (laws of the iterated logarithm). This type LIL has been established by Vasudeva and Divanji [13], Zinchenko [14] for delayed sums, by Chen and Huang [3] for geometric weighted sums, and by Chen [2] for weighted sums. Qi and Cheng [11] extended the Chover-type law of the iterated logarithm for the partial sums to the case where the underlying distribution is in th...
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