옌센 부등식

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  1. So we can prove the Jensen's inequality in this case.[1]
  2. Since many years Jensen’s inequality has received great interest.[2]
  3. In mathematics, Jensen's inequality, named after the Danish mathematician Johan Jensen, relates the value of a convex function of an integral to the integral of the convex function.[3]
  4. The classical form of Jensen's inequality involves several numbers and weights.[3]
  5. Jensen's inequality can be proved in several ways, and three different proofs corresponding to the different statements above will be offered.[3]
  6. This finite form of the Jensen's inequality can be proved by induction: by convexity hypotheses, the statement is true for n = 2.[3]
  7. Putting the identity function for , the inequality in (19) is reduced to If and , the above inequality represents the Jensen inequality.[4]
  8. This yields a natural question: under which conditions on in the -expectation does Jensen's inequality hold for any convex function?[5]
  9. again, we can get Hence, Jensen's inequality for holds in general.[5]
  10. # example of repeated trials of Jensen's Inequality from numpy .[6]
  11. In many cases, we want to say something about the expected value of g of X, and Jensen's inequality allows us to do that.[7]
  12. Jensen’s inequality has relevance in every field of biology that includes nonlinear processes.[8]
  13. E 1 , which shows how sharp the Jensen inequality is.[9]
  14. E 2 , which shows that the Jensen inequality is quite sharp.[9]
  15. The Jensen inequality has numerous applications in engineering, economics, computer science, information theory, and coding; it has been derived for convex and generalized convex functions.[9]
  16. Numerical experiments not only confirm the sharpness of the Jensen inequality but also provide evidence for the tightness of the bound given in (2.15) for the Jensen gap.[9]
  17. This article proposes a new sharpened version of Jensen's inequality.[10]
  18. AB - This article proposes a new sharpened version of Jensen's inequality.[10]
  19. In effect, we compared the mean of the function versus the function of the mean; using this ratio as a way of quantifying the magnitude of Jensen’s inequality.[11]

소스

  1. ↑ Jensen's Inequality
  2. ↑ Refinement of Jensen’s inequality and estimation of f - and Rényi divergence via Montgomery identity
  3. ↑ 3.0 3.1 3.2 3.3 Jensen's inequality
  4. ↑ The Applications of Functional Variants of Jensen's Inequality
  5. ↑ 5.0 5.1 Jensen's Inequality for Generalized Peng's -Expectations and Its Applications
  6. ↑ A Gentle Introduction to Jensen’s Inequality
  7. ↑ Part II: Inference & Limit Theorems
  8. ↑ Jensen’s inequality predicts effects of environmental variation
  9. ↑ 9.0 9.1 9.2 9.3 New Estimates for the Jensen Gap Using s-Convexity With Applications
  10. ↑ 10.0 10.1 Sharpening Jensen's Inequality
  11. ↑ Jensen’s Inequality and the Impact of Short-Term Environmental Variability on Long-Term Population Growth Rates

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  • [{'LOWER': 'jensen'}, {'LOWER': "'s"}, {'LEMMA': 'inequality'}]
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