Web12 nov 2024 · The Jensen inequality is a widely used tool in a multitude of fields, such as for example information theory and machine learning. It can be also used to derive other … http://users.mat.unimi.it/users/libor/AnConvessa/Jensen.pdf
proof of Jensen’s inequality - PlanetMath
WebOur first bound is perhaps the most basic of all probability inequalities, and it is known as Markov’s inequality. Given its basic-ness, it is perhaps unsurprising that its proof is essentially only one line. Proposition 1 (Markov’s inequality). LetZ ≥ 0 beanon-negativerandom variable. Thenforallt ≥ 0, P(Z ≥ t) ≤ E[Z] t. WebChapter 2, Lecture 4: Jensen’s inequality February 11, 2024 University of Illinois at Urbana-Champaign 1 Jensen’s inequality Jensen’s inequality ... write an induction … dha us298 training
A PROOFOF JENSEN’SINEQUALITY - Project Euclid
WebIn this paper, we present more proofs of the new Steffensen's inequality for convex functions. First, we provide separate proofs for continuous functions followed by a … 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 … Visualizza altro 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 … Visualizza altro Form involving a probability density function Suppose Ω is a measurable subset of the real line and f(x) is a non-negative function such that $${\displaystyle \int _{-\infty }^{\infty }f(x)\,dx=1.}$$ Visualizza altro • Jensen's Operator Inequality of Hansen and Pedersen. • "Jensen inequality", Encyclopedia of Mathematics, EMS Press, 2001 [1994] Visualizza altro 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 … Visualizza altro • Karamata's inequality for a more general inequality • Popoviciu's inequality • Law of averages Visualizza altro Web17 nov 2024 · Modified 1 year, 4 months ago. Viewed 423 times. 2. I want to prove the conditionnal Jensen's inequality. Let ( Ω, H, P) be a probability space, G ⊂ H a sub … cifom mediatheque