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《Mathematics in Practice and Theory》 2013-17
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Chung Type Strong Laws of Large Numbers and Applications

ZHANG Li-na;YAN Guang-zhou;CHEN Jun-ying;College of Science,Agricultural University of Hebei;  
In this paper,a simplified proof of Chung type strong law of large numbers has been established.And in the proof,neither the martingale convergence theorem nor the three series theorem is used.As applying of Chung type strong laws,some strong laws of large numbers and convergence rates for arbitrary stochastic adapted sequences have been obtained.These theorems and corollaries have extended the strong laws of large numbers established by Cantrell and Rosalsky and the convergence results obtained by Freedman(1974).For random sequences valuing on some point-set,the relationships of frequency and transition probability have been established.In all the paper,no condition of independence or on the distribution of random variables are required except the conditions on moments of random variables.
【Fund】: 河北省自然基金(E2008000357 F2010001044);; 河北农业大学非生命学科基金
【CateGory Index】: O211.4
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