The purpose of this paper is to give a selective survey on recent progress in random metric theory and its applications to conditional risk measures.This paper includes eight sections.Section 1 is a longer introductio...The purpose of this paper is to give a selective survey on recent progress in random metric theory and its applications to conditional risk measures.This paper includes eight sections.Section 1 is a longer introduction,which gives a brief introduction to random metric theory,risk measures and conditional risk measures.Section 2 gives the central framework in random metric theory,topological structures,important examples,the notions of a random conjugate space and the Hahn-Banach theorems for random linear functionals.Section 3 gives several important representation theorems for random conjugate spaces.Section 4 gives characterizations for a complete random normed module to be random reflexive.Section 5 gives hyperplane separation theorems currently available in random locally convex modules.Section 6 gives the theory of random duality with respect to the locally L0-convex topology and in particular a characterization for a locally L0-convex module to be L0-pre-barreled.Section 7 gives some basic results on L0-convex analysis together with some applications to conditional risk measures.Finally,Section 8 is devoted to extensions of conditional convex risk measures,which shows that every representable L∞-type of conditional convex risk measure and every continuous Lp-type of convex conditional risk measure(1 ≤ p < +∞) can be extended to an L∞F(E)-type of σ,λ(L∞F(E),L1F(E))-lower semicontinuous conditional convex risk measure and an LpF(E)-type of T,λ-continuous conditional convex risk measure(1 ≤ p < +∞),respectively.展开更多
The paper proposes a new text similarity computing method based on concept similarity in Chinese text processing. The new method converts text to words vector space model at first, and then splits words into a set of ...The paper proposes a new text similarity computing method based on concept similarity in Chinese text processing. The new method converts text to words vector space model at first, and then splits words into a set of concepts. Through computing the inner products between concepts, it obtains the similarity between words. The new method computes the similarity of text based on the similarity of words at last. The contributions of the paper include： 1） propose a new computing formula between words; 2） propose a new text similarity computing method based on words similarity; 3） successfully use the method in the application of similarity computing of WEB news; and 4） prove the validity of the method through extensive experiments.展开更多
基金supported by National Natural Science Foundation of China (Grant No.10871016)
文摘The purpose of this paper is to give a selective survey on recent progress in random metric theory and its applications to conditional risk measures.This paper includes eight sections.Section 1 is a longer introduction,which gives a brief introduction to random metric theory,risk measures and conditional risk measures.Section 2 gives the central framework in random metric theory,topological structures,important examples,the notions of a random conjugate space and the Hahn-Banach theorems for random linear functionals.Section 3 gives several important representation theorems for random conjugate spaces.Section 4 gives characterizations for a complete random normed module to be random reflexive.Section 5 gives hyperplane separation theorems currently available in random locally convex modules.Section 6 gives the theory of random duality with respect to the locally L0-convex topology and in particular a characterization for a locally L0-convex module to be L0-pre-barreled.Section 7 gives some basic results on L0-convex analysis together with some applications to conditional risk measures.Finally,Section 8 is devoted to extensions of conditional convex risk measures,which shows that every representable L∞-type of conditional convex risk measure and every continuous Lp-type of convex conditional risk measure(1 ≤ p < +∞) can be extended to an L∞F(E)-type of σ,λ(L∞F(E),L1F(E))-lower semicontinuous conditional convex risk measure and an LpF(E)-type of T,λ-continuous conditional convex risk measure(1 ≤ p < +∞),respectively.
基金Supported by the China Postdoctoral Science Foundation (Grant No. 20060400002)the Sichuan Youth Science and Technology Foundation of China (Grant No. 08JJ0109)+2 种基金the National Natural Science Foundation of China (Grant Nos.60473051, 60503037)the National High-tech Re- search and Development of China (Grant No. 2006AA01Z230)the Natural Science Foundation of Beijing Natural Science Foundation (Grant No. 4062018)
文摘The paper proposes a new text similarity computing method based on concept similarity in Chinese text processing. The new method converts text to words vector space model at first, and then splits words into a set of concepts. Through computing the inner products between concepts, it obtains the similarity between words. The new method computes the similarity of text based on the similarity of words at last. The contributions of the paper include： 1） propose a new computing formula between words; 2） propose a new text similarity computing method based on words similarity; 3） successfully use the method in the application of similarity computing of WEB news; and 4） prove the validity of the method through extensive experiments.
