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引入了原子鞅与正则原子鞅概念、并研究了两类Banach空间值鞅Hardy空间的原子分解和有限鞅的稠密性,所得结论揭示了鞅Hardy空间正则原子鞅分解的存在性,有限鞅的稠密性和Banach空间的一致光滑性(或一致凸性)三者之间的内在联系. 相似文献
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Several theorems for atomic decompositions of Banach-space-valued martingales are proved. As their applications, the relationship
among some martingale spaces such asH
α(X) andρ
H
α in the case 0< α⩽ are studied. It is shown that there is a close connection between the results and the smoothness and convexity
of the value spaces.
Project supported by the National Natural Science Foundation of China (Grant No. 19771063). 相似文献
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本文研究了B值弱Hardy两指标鞅空间的原子分解理论,利用原子分解的方法, 获得了B值弱Hardy两指标鞅空间的相互嵌入关系,所得结果联系于Banach空间的几何性质. 相似文献
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本文对几类B值小指标鞅空间建立了原子分解定理,利用原子分解讨论了它们之间的相互嵌入关系,其原子分解的存在性和它们之间的关系均与Banach空间的凸性和光滑性有密切联系. 相似文献
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应用原子分解方法,讨论了一类Banach空间值鞅Hardy空间的实内插,推广了Weisz[3]中的相应结论 相似文献
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本应用解析鞅的一类特殊的不等式给出了具有AUMD性质的复Banach空间的某些特征。 相似文献
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In this paper atomic decompositions for two-parameter vector-valued martingales are given. With the help of the atomic decompositions
the relations between the mutual embedding of two-parameter vector-valued martingale spaces and geometric properties of Banach
spaces are investigated. Our study shows that geometric properties of Banach spaces determine the embedding of martingale
spaces and conversely the latter can characterize the former.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
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向量值Lipschitz鞅空间p_λ~β(X)和p_∧~β(X) 总被引:1,自引:0,他引:1
本文研究了Banach空间值Lipchitz 鞅空间。与与 之间的相互嵌入关系,以及与小指标Hardy 鞅空间,的共轭空间之间的相互嵌入关系,其结果与值空间的凸性和光滑 性有着密切的联系, 相似文献
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本文给出B值拟鞅的概率不等式与集合不等式,并用它们刻划了B空间的p可光滑性及q可凸性,作为应用,还证明了B值拟鞅的强大数律,收敛速度及极大值函数的可积性。 相似文献
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Wojciech Herer 《Set-Valued Analysis》1997,5(2):147-157
We prove extension of classical convergence theorem of P. Lévy for martingales of random subsets of a metric space of negative curvature. 相似文献
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Coenraad C.A. Labuschagne 《Journal of Mathematical Analysis and Applications》2008,342(2):780-797
Denote by cf(X) the set of all nonempty convex closed subsets of a separable Banach space X. Let (Ω,Σ,μ) be a complete probability space and denote by (L1[Σ,cf(X)],Δ) the complete metric space of (equivalence classes of a.e. equal) integrably bounded cf(X)-valued functions. For any preassigned filtration (Σi), we describe the space of Δ-convergent integrably bounded cf(X)-valued martingales in terms of the Δ-closure of in L1[Σ,cf(X)]. In particular, we provide a formula to calculate the join of two such martingales and the positive part of such a martingale. Our object is achieved by considering the more general setting of a near vector lattice (S,d), endowed with a Riesz metric d. By means of Rådström's embedding theorem for such spaces, a link is established between the space of convergent martingales in S and the space of convergent martingales in the Rådström completion R(S) of S. This link provides information about the former space of martingales, via known properties of measure-free martingales in Riesz normed vector lattices, applicable to R(S). We also apply our general results to the spaces of Δ-convergent ck(X)-valued martingales, where ck(X) denotes the set of all nonempty convex compact subsets of X. 相似文献
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Un Cig Ji 《Proceedings Mathematical Sciences》2006,116(4):489-505
In this paper a quantum stochastic integral representation theorem is obtained for unbounded regular martingales with respect
to multidimensional quantum noise. This simultaneously extends results of Parthasarathy and Sinha to unbounded martingales
and those of the author to multidimensions.
Dedicated to Professor Kalyan B Sinha on the occasion of his 60th birthday 相似文献
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平削算子生成的B值鞅空间及其原子分解 总被引:3,自引:3,他引:0
对于一系列由平削算子生成的Banach空间值鞅空间建立了原子分解定理 ,并以此为工具讨论了它们之间的相互嵌入关系 ,其结果与Banach空间的凸性和光滑性有密切联系 . 相似文献
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复拟Banach空间的PL一致光滑性及其鞅刻划 总被引:2,自引:0,他引:2
本文引进了空间的PL一致光滑性与复对称鞅,证明了等价赋范定理,得到了一系列关于PL一致光滑空间的复对称鞅不等式,并应用复对称鞅的大数定律给出了值空间的PL一致光滑性的刻划。 相似文献
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Masato Kikuchi 《Mathematische Nachrichten》2008,281(5):697-709
We give a characterization of those Banach function spaces in which the Davis inequality for martingales is valid. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献