Sur les fonctions convexes et les inégalités entre les valeurs moyennes¶
Jensen, J. L. W. V. (1906). Sur les fonctions convexes et les inégalités entre les valeurs moyennes. Acta Mathematica, 175-193.
Cited by¶
2 citations across 2 artifacts.
Each citation links to the sentence it supports in the citing article.
Primes¶
- Antifragility
- The property is dose-dependent and curvature-dependent: it holds within a tolerance window beyond which the same stressors that strengthen become destructive, a non-linearity Jensen's inequality makes precise for any convex transformation of a fluctuating input.
This sourceEstablishes Jensen's inequality for convex functions, E[f(x)] ≥ f(E[x]); the basis for why increasing the variance of a fluctuating input raises the expected output of a convex response at fixed mean (and lowers it for a concave one), making antifragility's dose-/curvature-dependence precise; supports markers 063, 074.
- The property is dose-dependent and curvature-dependent: it holds within a tolerance window beyond which the same stressors that strengthen become destructive, a non-linearity Jensen's inequality makes precise for any convex transformation of a fluctuating input.
Mechanisms¶
- Inter-Event Interval Estimator
- Because the estimate is the reciprocal of a single noisy interval, one missing or spurious event corrupts it completely, and — more insidiously — averaging reciprocals systematically overstates the rate
This sourceFor positive varying intervals, Jensen’s inequality establishes that the mean reciprocal exceeds the reciprocal of the mean.
- Because the estimate is the reciprocal of a single noisy interval, one missing or spurious event corrupts it completely, and — more insidiously — averaging reciprocals systematically overstates the rate
Verification¶
This reference passed the adversarial substantiation pipeline: it was checked to exist and to support the claim it is attached to. See how references were verified.
Registry ID ref:3658beca7279 · see in the full table