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 本文說明在金融、土木工程以及風險管理常用的「設計點重要抽樣法」，其理論可以被整合入「高維度嵌入相對熵重要抽樣法」。
 This paper demonstrates that the design-point importance sampling, which is prevalent in civil and financial engineering as well as risk management, can be theoretically justified by using the high-dimensional embedding entropy-based importance sampling.
 [1] Chuan-Hsiang Han. Optimal variance minimization: A new importance samplingmethod by high-dimensional embedding. working paper, 3 2014.[2] Munehisa Fujita and Rüdiger Rackwitz. Updating first-and second-order reliabilityestimates by importance sampling. Structural Engineering and Earthquake Engineering,JSCE, 5(1):31s–37s, 1988.[3] ComitéEuropéen du Béton. First order reliability concepts for design codes. BulletinD’Information, (112Joint), 1976.[4] Kok-Kwang Phoon and Farrokh Nadim. Modeling non-gaussian random vectorsfor form: State-of-the-art review. In International workshop on risk assessment insite characterization and geotechnical design. India Institute of Science, Bangalore,India, pages 26–27, 2004.[5] Zakoua Guédé, B Sudret, and M Lemaire. Life-time reliability based assessmentof structures submitted to thermal fatigue. International journal of fatigue, 29(7):1359–1373, 2007.[6] Omri Sarig. Lecture notes on ergodic theory, 2009.[7] Armen Der Kiureghian et al. First-and second-order reliability methods. Engineeringdesign reliability handbook, pages 14–1, 2005.[8] Rabi De and Tanya Tamarchenko. System and method for determining value-at-riskusing form/sorm, 2001.29[9] DH Ebberle, LE Newlin, S Sutharshana, and Nicholas R Moore. Alternative computationalapproaches for probabilistic fatigue analysis. AIAA Paper, 1359:1995,1995.[10] Oluwasanmi Koyejo and Joydeep Ghosh. A representation approach for relative entropyminimization with expectation constraints. In ICML Workshop on Divergencesand Divergence Learning (WDDL), 2013.[11] Yasemin Altun and Alex Smola. Unifying divergence minimization and statisticalinference via convex duality. In Learning theory, pages 139–153. Springer, 2006.[12] Imre Csiszár. I-divergence geometry of probability distributions and minimizationproblems. The Annals of Probability, pages 146–158, 1975.[13] Definitions and basic properties. In An Introduction to Copulas, Springer Series inStatistics, pages 7–49. Springer New York, 2006.[14] Solomon Kullback. A lower bound for discrimination information in terms of variation(corresp.). Information Theory, IEEE Transactions on, 13(1):126–127, 1967.[15] Chia-Ping Chen. Entropy and mutual information–notes on information theory.[16] Christian Léonard. Minimization of entropy functionals. Journal of MathematicalAnalysis and applications, 346(1):183–204, 2008.[17] O. Ditlevsen and H.O. Madsen. Structural Reliability Methods. Series; 9. Wiley,1996.[18] SK Au, C Papadimitriou, and JL Beck. Reliability of uncertain dynamical systemswith multiple design points. Structural Safety, 21(2):113–133, 1999.[19] Steven E Shreve. Stochastic calculus for finance II: Continuous-time models, volume11. Springer Science & Business Media, 2004.[20] Neil Shephard, Ole E Barndorff-Nielsen, et al. Basics of levy processes. Technicalreport, 2012.30[21] Dorje C Brody, Lane P Hughston, and Xun Yang. Signal processing with levy information.arXiv preprint arXiv:1207.4028, 2012.31
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