共查询到18条相似文献,搜索用时 419 毫秒
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本文讨论了集值拟鞅和集值一致渐近鞅,证明了集值拟鞅与集值一致渐近鞅的选样定理,对于集值一致渐近鞅得到了一些收敛性结果,并由此刻化了空间的 Radon-Nikodym性质. 相似文献
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关于集值Pramart的某些结果 总被引:10,自引:1,他引:9
本文引进了Boohner可积函数空间L~1[Ω;X]中子集的可分解包的概念,给出了集值随机变量族本性上确界的定义及基本性质。以此为基础,研究了集值Pramart的性质;用类似于实值Snell包的方法给出了集值superpramart的上鞅逼近,证明了集值superpramart在Kuratowski-Mosco意义下的收敛定理。 相似文献
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B值渐近鞅是B值鞅的重要推广,它保持了鞅的一些是一性质,然后对B值渐近鞅的局部收敛性很少有文献论及。本文利用B值渐近鞅的Doob分解,对B值渐近鞅的局部收敛性作些探讨,得到了B值渐近鞅局部收敛性的几个结果,它们是鞅的有关结论的推广与改进。 相似文献
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闭区间值鞅及模糊数值鞅 总被引:1,自引:0,他引:1
集值上鞅、下鞅和鞅的收敛定理已有不少文章进行了研究[1]、[2][3]。但在这些文章中,集值上(下)鞅并不以经典的上(下)鞅为其特款。在本文中,我们定义了以经典上(下)鞅为其特款的闭区间值上(下)鞅,并讨论了它们的性质及其收敛定理。本文还在此基础上讨论了模糊数值鞅。 相似文献
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集值上鞅的收敛定理及 Riesz 分解 总被引:17,自引:0,他引:17
本文给出了集值鞅的进一步性质;建立了集值上鞅外穿不等式;证明了一个集值上鞅收敛定理;研究了集值上鞅的 Riesz 分解. 相似文献
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李高明 《纯粹数学与应用数学》2010,26(3):363-366
在X^*可分的条件下,首先讨论了集值Pramart有关支撑函数和距离函数的性质,利用支撑函数和距离函数研究了集值Pramart鞅逼近,在此基础上,给出了集值Pramart的一类鞅分解. 相似文献
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集值下(上)鞅的 Doob 分解 总被引:8,自引:0,他引:8
本文研究集值下(上)鞅的 Doob 分解.我们得到一些确保 Doob 分解存在的充要条件,并给出例子说明并非所有集值下(上)鞅都有 Doob 分解. 相似文献
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In a separable Banach space, for set-valued martingale, several equivalent conditions based on the measurable selections are discussed, and then, in an M-type 2 Banach space, at first we define single valued stochastic integral by the differential of a real valued Brownian motion, after that extend it to set-valued case. We prove that the set-valued stochastic integral becomes a set-valued submartingale, which is different from single valued case, and obtain the Castaing representation theorem for the set-valued stochastic integral, which is applicable for set-valued stochastic differential equations. 相似文献
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In this paper, we shall firstly illustrate why we should consider integral of a stochastic process with respect to a set-valued square integrable martingale. Secondly, we shall prove the representation theorem of set-valued square integrable martingale. Thirdly, we shall give the definition of stochastic integral of a stochastic process with respect to a set-valued square integrable martingale and the representation theorem of this kind of integrals. Finally, we shall prove that the stochastic integral is a set-valued sub-martingale. 相似文献
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The present paper contains a martingale representation theorem for set-valued martingales defined on a filtered probability space with a filtration generated by a Brownian motion. It is proved that such type martingales can be defined by some generalized set-valued stochastic integrals with respect to a given Brownian motion. The main result of the paper is preceded by short part devoted to the definition and some properties of generalized set-valued stochastic integrals. 相似文献
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C. S. Lalitha 《Numerical Functional Analysis & Optimization》2013,34(7-8):897-909
Using the concept of supremum/infimum of a set, defined in terms of the closure of the set, we introduce the notions of conjugate and biconjugate maps as well as that of subgradients of a set-valued map. Conjugate duality results are also established for a set-valued optimization problem. 相似文献
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假定(X,‖·‖)为实Banach空间,X*为其对偶空间,X*可分.给出了集值上鞅几种不同的Doob分解概念,利用支撑函数研究了集值上鞅在各种分解意义下可Doob分解的充分必要条件. 相似文献
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Andreas H. Hamel 《Set-Valued and Variational Analysis》2009,17(2):153-182
It is proven that a proper closed convex function with values in the power set of a preordered, separated locally convex space
is the pointwise supremum of its set-valued affine minorants. A new concept of Legendre–Fenchel conjugates for set-valued
functions is introduced and a Moreau–Fenchel theorem is proven. Examples and applications are given, among them a dual representation
theorem for set-valued convex risk measures.
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