The law of the iterated logarithm and Marcinkiewicz law of large numbers forB-valuedU-statistics |
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| Authors: | Zhonggen Su |
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| Affiliation: | (1) Department of Mathematics, Hangzhou University, 310028 Zhejiang, China;(2) Institute of Mathematics, Fudan University, 200433 Shanghai, China |
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| Abstract: | Suppose thatB is a separable Banach space and (S,l,P) a probability space.H is a measurable symmetric kernel function fromSm intoB. In this paper we shall further study some limit theorems forB-valuedU-statisticsUmnH based onP andH. Special attention is paid upon the Marcinkiewicz type law of large numbers and the law of the iterated logarithm. Our results can be regarded as extensions of corresponding results for sums of independentB-valued random variables toU-statistics.Research supported by National Natural Science Foundation of China and Zhejiang Province. |
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| Keywords: | B-U-statistics decoupling inequality law of large numbers law of the iterated logarithm |
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