共查询到19条相似文献,搜索用时 57 毫秒
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本文研究了拟概率空间上的强大数定律问题.利用类比的方法,在比概率测度空间更广范的拟概率空间上,提出了强大数定律的概念,获得了拟概率空间上强大数定律的相关结论,推广了强大数定律的研究范围和应用领域. 相似文献
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本文讨论(?,F)上的上概率ω(·)和下概率ω_c(·)以及它们的某些性质,并由上概率下随机变量序列的独立性、正则性,给出上概率下的中心极限定理,它是经典概率论中中心极限定理在非可加概率下的的推广. 相似文献
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利用初等方法研究Chebyshev多项式的性质,建立了广义第二类Chebyshev多项式的一个显明公式,并得到了一些包含第一类Chebyshev多项式,第一类Stirling数和Lucas数的恒等式. 相似文献
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马氏环境中马氏链的强大数定律 总被引:9,自引:0,他引:9
讨论了具有离散参数的马氏环境中马氏链的强大数定律,并给出了加在链和过程样本函数上的充分条件.同时深入研究了Rθ-链,得到马氏环境中马氏链强大数定律成立的充分条件. 相似文献
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设Xn(n≥0)是在可数集En中取值的随机变量,An(x0,…,xn-1)是定义在E0×…×En-1上的正值函数,{φn(x),n≥1}是(-∞,+∞)上的正值连续偶函数序列,且当|x|增加时,φn(x)/|x|↑,φn(x)/x2↓.本文给出了a.e.收敛的一个充分条件.所得结果是一类经典强大数定律的推广.证明中发展了第一作者所提出的研究离散随机变量序列强极限定理的分析方法. 相似文献
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切贝舍夫是俄国十九世纪最伟大的数学家之一,他第一个主张概率论的极限定理应该严格的证明,并尽可能精确地确定偏离极限的估计量,这在方法论上引起了很大变化.其创立的切贝舍夫不等式和切贝舍夫大数定律是概率论极限理论的基础,从而使概率论成为严密数学分支.切贝舍夫的概率思想是在一定数学文化背景产生的,尤其是法国数学文化对其发展的形成有着深刻影响. 相似文献
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设(Ω,F,μ)为概率空间,v为(Ω,F)上的有限测度的密度定理,并研究了v的维数及维数分布的若干性质。 相似文献
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《随机分析与应用》2013,31(4):1067-1083
Abstract The strong laws of large numbers with the convergence in the sense of the uniform Hausdorff metric for stationary sequences of random upper semicontinuous functions is established. This approach allows us to deduce many results on the convergence in uniform Hausdorff metric of random upper semicontinuous functions from the relevant results on real-valued random variables that appear as their support functions. 相似文献
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Bogdanskii V. Yu. Klesov O. I. Molchanov I. 《Methodology and Computing in Applied Probability》2021,23(2):461-470
Methodology and Computing in Applied Probability - We prove the strong law of large numbers for random signed measures. The result is uniform over a family of subsets under mild assumptions. 相似文献
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Samy Abbes 《Journal of Theoretical Probability》2017,30(4):1692-1725
We consider the framework of Bernoulli measures for heap monoids. We introduce in this framework the notion of asynchronous stopping time, which generalizes the notion of stopping time for classical probabilistic processes. A strong Bernoulli property is proved. A notion of cut-invariance is formulated for convergent ergodic means. Then, a version of the strong law of large numbers is proved for heap monoids with Bernoulli measures. We study a sub-additive version of the law of large numbers in this framework. 相似文献
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This note is devoted to introduce a new concept of conditionally dominated random variables.Under suitable restrict conditions,a general strong law of large numbers for arbitrary continuous random variables is obtained. 相似文献
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Jakša Cvitanić Jin Ma Jianfeng Zhang 《Stochastic Processes and their Applications》2012,122(8):2781-2810
We consider a model of correlated defaults in which the default times of multiple entities depend not only on common and specific factors, but also on the extent of past defaults in the market, via the average loss process, including the average number of defaults as a special case. The paper characterizes the average loss process when the number of entities becomes large, showing that under some monotonicity conditions the limiting average loss process can be determined by a fixed point problem. We also show that the Law of Large Numbers holds under certain compatibility conditions. 相似文献
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B值混合随机场的强大数律 总被引:13,自引:0,他引:13
本文讨论了取值于p型空间(1≤p<2)上的混合随机场的强大数律和完全收敛性问题,获得了与独立同分布情形相类似的结果;改进了张立新(1998)的结果,并对该文中提出的一些问题作了回答.特别对ρ-混合,ρ*-混合实值随机序列部分和的大数定律给出了必要条件. 相似文献
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Pedro Terán 《Journal of Theoretical Probability》2016,29(2):349-358
We prove a strong law of large numbers for random closed sets in a separable Banach space. It improves upon and unifies the laws of large numbers with convergence in the Wijsman, Mosco and slice topologies, without requiring extra assumptions on either the properties of the space or the kind of sets that can be taken on by the random set as values. 相似文献