WebOct 9, 2024 · Jensen’s inequality for the univariate case is very common and is relatively simple to prove. In addition, there is also a more generalized multivariate Jensen’s inequality, and I was not able to find any proof from the Internet. In this blog post, I would like to quickly derive the proof to the univariate and multivariate Jensen’s ...
Jensen
Web수학에서 옌센 부등식(영어: Jensen’s inequality)은 기댓값의 볼록 함수와 볼록 함수의 … WebApr 13, 2024 · 확률의 절대부등식, Inequality. 스터디/확률과 통계 2024. 4. 13. 10:19. 확률 (특히 기댓값)과 관련된 부등식들이 많이 알려져 있다. 이중 4가지 부등식에 대하여 다룬다. 각 부등식 마다 확률변수의 정의나 범위가 다르므로 주의한다. helen m foglesong del city ok
Jensen
http://www.sef.hku.hk/~wsuen/teaching/micro/jensen.pdf 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. It was proved by Jensen in 1906, building on an earlier proof of the same inequality for doubly-differentiable functions by Otto Hölder … See more The classical form of Jensen's inequality involves several numbers and weights. The inequality can be stated quite generally using either the language of measure theory or (equivalently) probability. In the … See more Form involving a probability density function Suppose Ω is a measurable subset of the real line and f(x) is a … See more • Jensen's Operator Inequality of Hansen and Pedersen. • "Jensen inequality", Encyclopedia of Mathematics, EMS Press, 2001 [1994] • Weisstein, Eric W. "Jensen's inequality". MathWorld. See more Jensen's inequality can be proved in several ways, and three different proofs corresponding to the different statements above will be offered. Before embarking on these … See more • Karamata's inequality for a more general inequality • Popoviciu's inequality • Law of averages See more WebFeb 22, 2015 · for every x ∈ X. Integrating (2) gives Jensen's inequality, and it follows that we have the equality. ∫Xϕ ∘ fdμ = ϕ(∫Xfdμ) if and only if we have equality a.e. in (2). That we have equality a.e. in (2) means that ϕ coincides with an affine function on [the convex hull of] the essential range of f, but ϕ need not be affine globally ... helen metcalf obituary syracuse