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Radon-Nikodym Theorem in Signed Loeb Space 被引量：3

Radon-Nikodym Theorem in Signed Loeb Space
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摘要 This paper gives the Radon-Nikodym theorem in signed Loeb space under 1-saturated nonstandard model. First,the nonstandard characterization of absolute continuity is discussed,on which Radon-Nikodym theorem in signed Loeb space is obtained. Then,some facts about a finite signed Loeb measure and its variation are shown. This paper gives the Radon-Nikodym theorem in signed Loeb space under 1-saturated nonstandard model. First,the nonstandard characterization of absolute continuity is discussed,on which Radon-Nikodym theorem in signed Loeb space is obtained. Then,some facts about a finite signed Loeb measure and its variation are shown.
作者 MA Chunhui LI Shenggang SHI Yanwei
机构地区 College of Mathematics and Information Science School of Science Department of Basic Courses
出处 《Wuhan University Journal of Natural Sciences》 CAS 2010年第1期21-24,共4页 武汉大学学报（自然科学英文版）
基金 Supported by the Natural Science Foundation of Shaanxi Province(2007A12)
关键词 signed Loeb measure Loeb space absolutely continuity Radon-Nikodym theorem VARIATION signed Loeb measure Loeb space absolutely continuity Radon-Nikodym theorem variation
分类号 O174.12 [理学—基础数学] O174 [理学—基础数学]
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参考文献13

  • 1Milo? Ziman,Pavol Zlato?.Hyperfinite Dimensional Representations of Spaces and Algebras of Measures[J]. Monatshefte für Mathematik . 2006 (3)
  • 2Robert M. Anderson.A non-standard representation for Brownian Motion and It? integration[J]. Israel Journal of Mathematics . 1976 (1-2)
  • 3Robinson A.Nonstandard Analysis. . 1963
  • 4Keisler H J.An infinitesimal approach to stochastic analysis. Memoirs of the American Mathematical Society . 1984
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  • 6Cohn D L.Measure Theory. . 1980
  • 7Chen Dongli,Feng Hanqiao.Signed Loeb measure and im- age Loeb measure. Journal of Shaanxi Normal Uuinver- sity . 1996
  • 8Chen Dongli.Radon-Nikodym derivative on Loeb space. Journal of Mathematical . 1997
  • 9Loeb PA.Conversion from nonstandard to standard measure spaces and applications in probability theory. Transactions of the American Mathematical Society . 1975
  • 10Cutland,N.Nonstandard measure theory and its applications. Bulletin of the London Mathematical Society . 1983

同被引文献19

  • 1F. Black, M. Scholes. The pricing of options and corporate liabilities [ J ]. Journal of Political Economy, 1973 ( 81 ) : 637 - 654.
  • 2Oldrich vasicek. An equilibrium characterization of the term structure [ J ]. Journal of Financial Economics, 1977 (5) : 177 - 188.
  • 3F. A Longstaff, E. S. Schwartz. Valuing credit derivatives [ J ]. The Journal of Fixed Income, 1995 (5) .6 - 12.
  • 4Yan Haifeng, Chen Chunsheng. Girsanov theorem and its application in option pricing[ J]. Henan Normal University Journal of Natural Sciences, 2003 (31) : 123 - 128.
  • 5F. A Longstaff, E. S. Schwartz. Valuing credit derivatives[J]. The Journal of Fixed Income, 1995, (5): 6-12.
  • 6Oldrich vasicek. An equilibrium characterization of the term structure[J]. Journal of Financial Economics,1977,5:177-188.
  • 7Yan Haifeng, Chen Chunsheng. Girsanov theorem and its application in option pricing[J]. Henan Normal University Journal of Natural Sciences, 2003,31: 123-128.
  • 8Robinson A. Nonstandard analysis[M]. Amsterdam :North-Holland, 1963.
  • 9Akiyama, Hiroshi. Nonstandard solvability for linear operators between sections of vector bundles[J]. Proc. Amer. Math. Soc. ,2000,128(7) :2129-2135.
  • 10Berger, Josef. On nonstandard product measure spaces[J]. Illinois J. Math. ,2002,46 : 319-330.

引证文献3

Wuhan University Journal of Natural Sciences
2010年 第1期

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