| 关于m-值随机序列广义随机选择的一个强极限定理 |
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| 引用本文： | 汪忠志,徐付霞. 关于m-值随机序列广义随机选择的一个强极限定理[J]. 数学季刊, 2003, 18(4): 343-348 |
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| 作者姓名： | 汪忠志 徐付霞 |
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| 作者单位： | [1]DepartmentofMathematicsandPhysics,AnhuiUniversityofTechnology,Ma‘anshan243002,China [2]DepartmentofMathematics,TangshanTeacher’sCollege,Tangshan063000,China |
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| 基金项目： | SupportedbytheEducationDepartmentofAnhuiProvince( 2 0 0 2kj0 5 4) |
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| 摘 要： | § 1. Introduction ConsiderasequenceofBernoullitrials ,andsupposethatateachtrialthebettorhasthefreechoiceofwhetherornottobet.Asystemconsistsinfixedrulesselectingthosetrialsonwhichtheplayeristobet.ThetheoremongamblingsystemassertsthatunderanysystemthesuccessivebetsformasequenceofBernoullitrialwithunchangedprobabilityforsuccess.TheimportanceofthisstatementwasfirstrecognizedbyvonMises,whointroducedtheimpossibili tyofasuccessfulgamblingsystemasafundamentalaxiom(cf.[1 ],[2 ],[3],[4]) .Thecon …
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| 关 键 词： | 强极限定理 广义随机选择 Bernoulli序列 随机变量 可微性 |
A Strong Limit Theorem on Generalized Random Selection for m-valued Random Sequences |
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| WANGZhong-zhi XUFu-xia. A Strong Limit Theorem on Generalized Random Selection for m-valued Random Sequences[J]. Chinese Quarterly Journal of Mathematics, 2003, 18(4): 343-348 |
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| Authors: | WANGZhong-zhi XUFu-xia |
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| Abstract: | In this paper, a strong limit theorem on gambling strategy for binary Bernoulli sequence, i.e.irregularity theorem, is extended to random selection for dependent m-valued random variables, via using a new method-differentiability on net. Furthermore, by allowing the selection function to take value in finite interval [-M, M], the conception of random selection is generalized. |
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| Keywords: | generalized random selection differentiability on net a.e.convergence |
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