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《数学的实践与认识》2017,(22)
讨论了非可加概率ω(·)和非可加期望E[·]的某些性质,并由上期望下随机变量的独立性概念,给出了上概率下的Chebyshev大数定律,它是经典概率论中Chebyshev大数定律在非可加概率下的推广. 相似文献
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关于~*-mixing随机变量序列的强大数定律 总被引:1,自引:0,他引:1
利用任意随机变量序列的强大数定律讨论 * -mixing随机变量序列的强大数定律 ,得到了该序列的一个强极限定理 ,推广了经典的 * mixing随机变量序列的强大数定律 .同时讨论了 m相依序列和独立随机变量序列的强大数定律 . 相似文献
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强大数定律的若干新结果 总被引:12,自引:0,他引:12
本文利用Hajek-Renyi型最大值不等式,获得了随机变量和的强大数定律和 收敛速度.作为应用,给出了某些相依随机变量和新的强大数定律. 相似文献
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对一类有界独立或相依的随机变量序列|ξn|,获得了它的伯努利大数定律、波雷尔强大数定律及常返性定理.作为应用,得出了Loève专著[1]中的推广的伯努利大数定律、常返性定理,改进了[1]中的推广的波雷尔强大数定律. 相似文献
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利用两两NQD列三级数定理的思想和Chebyshev不等式,研究了两两NQD列在一类广泛条件下的弱大数定律和一类加强条件下的强大数定律,得到了与独立情形一致的结果,还特别讨论了同分布情形,推广了相关文献的结果. 相似文献
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《数学的实践与认识》2013,(17)
利用逐项积分对Chung型强大数定律进行简单化证明,证明既不需要鞅收敛定理,也不需要三级数定理.应用Chung型强律,得到了随机序列的若于强大数定律和收敛速度等,这些定理和推论推广了Cantrell-Rosalsky强大数定律以及由Freedman(1974)建立的关于收敛速度的结果.这些结果除矩条件外,对随机变量的独立性和联合分布不作任何要求. 相似文献
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本文引进似然比作为离散随机变量序列相依性的一种度量,并利用这个概念给出一类在样本空间的某种子集上的强律,它包含若干通常的强大数定律为其特例。 相似文献
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本文证明了φ-混合随机变量的Er(o)ds-Rényi大数定律. 特别地,以概率1,WN1n=snf[n(N)t]-sn/h(N)的极限点集是相对紧的并与函数空间的大偏差速率函数相联系, 其中(x)是取值于Banach 空间的-混合随机变量,h(N)=[clog N]. 相似文献
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Fuzzy Random Variables: A Scalar Expected Value Operator 总被引:24,自引:5,他引:19
Fuzzy random variable has been defined in several ways in literature. This paper presents a new definition of fuzzy random variable, and gives a novel definition of scalar expected value operator for fuzzy random variables. Some properties concerning the measurability of fuzzy random variable are also discussed. In addition, the concept of independent and identically distributed fuzzy random variables is introduced. Finally, a type of law of large numbers is proved. 相似文献
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The problem of Robot Selection is of great relevance in the present times of automation. Traditionally such problems were addressed using conventional techniques of Multi Criteria Decision Making such as The Analytic Hierarchy Process (AHP) and The Multi Attribute Utility Theory (MAUT). This paper proposes a methodology for solving common Robot Selection problems using a modification of the conventional AHP by incorporating ‘Fuzzy Linguistic Variables’ in place of numbers. The methodology encapsulates creation of Fuzzy Interface for conversion of input and output variables into suitable linguistic variables. Further, employing the fuzzification process by assigning the linguistic variables to numerical values of the membership functions and formulating suitable decision rules, the procedure culminates into the defuzzification process for converting fuzzy output into crisp value and obtaining the result in the form of Fuzzy Score. The proposed model is explained using a numerical example. The paper also presents a validation of the proposed methodology over real world problems and provides directions for future research towards the end.Additional support was provided by the National Science Foundation. 相似文献
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吴善和 《数学的实践与认识》2005,35(9):134-139
利用Ho。lder不等式、Young不等式、Chebyshev不等式、幂平均不等式建立Radon不等式的指数推广形式,得到一个具有广泛应用价值的不等式.指出文[7]中给出的关于Radon不等式的推广结果是错误的,并在本文中作了修正. 相似文献
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Roman Witu?a 《Journal of Mathematical Analysis and Applications》2010,361(1):276-279
Taking advantage of Nadarajah's representation of modified Chebyshev polynomials by means of the random variable that has the Student's t distribution [S. Nadarajah, On modified Chebyshev polynomials, J. Math. Anal. Appl. 334 (2007) 1492-1494] the scope of this paper is the generation of the identities for the moments of linear rescaling random variables that have the Student's t distribution. 相似文献
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本文研究了NA随机变量的Egorov型强大数律.利用NA随机变量的概率不等式,得到了NA随机变量序列的Egorov型强大数律的一些等价条件,所获结果推广和改进了在独立随机变量序列的Egorov的结果和在NA随机变量序列已有的一些结果. 相似文献
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LiXin Zhang 《中国科学 数学(英文版)》2016,59(4):751-768
Classical Kolmogorov’s and Rosenthal’s inequalities for the maximum partial sums of random variables are basic tools for studying the strong laws of large numbers. In this paper, motived by the notion of independent and identically distributed random variables under the sub-linear expectation initiated by Peng (2008), we introduce the concept of negative dependence of random variables and establish Kolmogorov’s and Rosenthal’s inequalities for the maximum partial sums of negatively dependent random variables under the sub-linear expectations. As an application, we show that Kolmogorov’s strong law of larger numbers holds for independent and identically distributed random variables under a continuous sub-linear expectation if and only if the corresponding Choquet integral is finite. 相似文献
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刘静 《数学的实践与认识》2006,36(10):111-118
在sm a le点估计理论引导下,利用优序列方法,研究γ-条件下,变形chebyshev迭代方法在求解Banach空间中非线性方程F(x)=0时的收敛性问题,并给出了误差估计,而且通过一个积分方程实例比较了它和N ew ton法,导数超前计值的变形N ew ton法,避免导数求逆的变形N ew ton法的每步误差. 相似文献
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B. L. S. Prakasa Rao 《Annals of the Institute of Statistical Mathematics》2009,61(2):441-460
Some properties of conditionally independent random variables are studied. Conditional versions of generalized Borel-Cantelli
lemma, generalized Kolmogorov’s inequality and generalized Hájek-Rényi inequality are proved. As applications, a conditional
version of the strong law of large numbers for conditionally independent random variables and a conditional version of the
Kolmogorov’s strong law of large numbers for conditionally independent random variables with identical conditional distributions
are obtained. The notions of conditional strong mixing and conditional association for a sequence of random variables are
introduced. Some covariance inequalities and a central limit theorem for such sequences are mentioned. 相似文献
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《International Journal of Approximate Reasoning》2001,26(1):47-66
Fuzzy random variables have been introduced by Puri and Ralescu as an extension of random sets. In this paper, we first introduce a real-valued generalized measure of the “relative variation” (or inequality) associated with a fuzzy random variable. This measure is inspired in Csiszár's f-divergence, and extends to fuzzy random variables many well-known inequality indices. To guarantee certain relevant properties of this measure, we have to distinguish two main families of measures which will be characterized. Then, the fundamental properties are derived, and an outstanding measure in each family is separately examined on the basis of an additive decomposition property and an additive decomposability one. Finally, two examples illustrate the application of the study in this paper. 相似文献